mrffl_life_table Module Reference

Life table computations, and some US life table data. More...

Functions/Subroutines
real(kind=rk) pure function, public	survivors (age, life_table, cohort_size)
	Return \( l_x \) for the given age.
real(kind=rk) pure function, public	probability_of_death (age, life_table, cohort_size)
	Return \( q_x \) for the given age.
real(kind=rk) pure function, public	life_expectancy (age, life_table, cohort_size)
	Return \( e_x \) for the given age.
real(kind=rk) pure function, public	life_expectancy_at_birth (life_table, cohort_size)
	Return \( e_0 \).
real(kind=rk) pure function, public	probability_of_survival_n (age, n, life_table, cohort_size)
	Return \( _tp_x \) for the given age.
real(kind=rk) pure function, public	probability_of_survival_1 (age, life_table, cohort_size)
	Return \( p_x \) for the given age.
real(kind=rk) pure function, public	died (age, life_table, cohort_size)
	Return \( d_x \) for the given age.
real(kind=rk) pure function, public	person_years (age, life_table, cohort_size)
	Return \( L_x \) for the given age.
real(kind=rk) pure function, public	total_person_years (age, life_table, cohort_size)
	Return \( T_x \) for the given age.
real(kind=rk) pure function, public	mortality_rate (age, life_table, cohort_size)
	Return \( m_x \) for the given age.
real(kind=rk) pure function, public	age_all_dead (life_table, cohort_size)
	Return lowest age for which \( l_x=0 \).
integer(kind=ik) function, public	rand_age (age, life_table, cohort_size)
	Return random age for death given current age and life_table.
subroutine, public	life_table_print (out_io_unit, print_out, life_table, cohort_size)
	Print life table.

Variables
real(kind=rk), dimension(0:119), parameter, public	usss_m_lx_dat = [ 100000, 99414, 99372, 99345, 99323, 99304, 99289, 99275, 99262, 99250, 99238, 99225, 99211, 99195, 99173, 99143, 99098, 99035, 98949, 98840, 98715, 98579, 98433, 98275, 98106, 97926, 97734, 97530, 97316, 97089, 96850, 96601, 96342, 96073, 95797, 95512, 95218, 94916, 94603, 94277, 93937, 93582, 93211, 92825, 92423, 92003, 91564, 91100, 90608, 90083, 89523, 88926, 88289, 87606, 86874, 86089, 85248, 84347, 83386, 82361, 81272, 80112, 78882, 77582, 76215, 74786, 73296, 71749, 70141, 68468, 66732, 64927, 63046, 61080, 59018, 56849, 54543, 52126, 49598, 46958, 44198, 41342, 38409, 35420, 32385, 29314, 26234, 23175, 20178, 17298, 14571, 12029, 9707, 7640, 5863, 4386, 3198, 2271, 1572, 1060, 698, 448, 279, 169, 99, 56, 30, 16, 8, 4, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0]
	\( l_x \) for males as recorded in the 2021 period life table for the US Social Security Administration.
real(kind=rk), dimension(0:119), parameter, public	usss_f_lx_dat = [ 100000, 99494, 99455, 99432, 99415, 99400, 99388, 99378, 99367, 99358, 99348, 99338, 99327, 99314, 99298, 99279, 99256, 99227, 99192, 99150, 99105, 99055, 98999, 98939, 98873, 98802, 98725, 98643, 98555, 98462, 98361, 98252, 98135, 98008, 97873, 97730, 97579, 97420, 97252, 97075, 96887, 96687, 96474, 96247, 96008, 95756, 95489, 95203, 94897, 94568, 94215, 93837, 93433, 93000, 92537, 92040, 91503, 90924, 90303, 89635, 88915, 88142, 87313, 86427, 85490, 84502, 83470, 82389, 81248, 80041, 78758, 77393, 75934, 74369, 72686, 70872, 68895, 66764, 64485, 62059, 59469, 56714, 53803, 50741, 47530, 44170, 40672, 37065, 33386, 29698, 26043, 22471, 19042, 15814, 12847, 10192, 7890, 5956, 4385, 3149, 2208, 1509, 1003, 646, 402, 241, 139, 77, 40, 20, 9, 4, 2, 1, 0, 0, 0, 0, 0, 0]
	\( l_x \) for females as recorded in the 2021 period life table for the US Social Security Administration.
real(kind=rk), dimension(0:119), parameter, public	usss_m_qx_dat = [ 0.0058600, 0.0004200, 0.0002720, 0.0002250, 0.0001840, 0.0001570, 0.0001400, 0.0001280, 0.0001220, 0.0001230, 0.0001290, 0.0001380, 0.0001640, 0.0002200, 0.0003100, 0.0004460, 0.0006370, 0.0008680, 0.0011000, 0.0012700, 0.0013730, 0.0014880, 0.0016050, 0.0017140, 0.0018350, 0.0019630, 0.0020820, 0.0022020, 0.0023300, 0.0024570, 0.0025740, 0.0026830, 0.0027870, 0.0028810, 0.0029740, 0.0030740, 0.0031750, 0.0032950, 0.0034440, 0.0036080, 0.0037800, 0.0039580, 0.0041440, 0.0043370, 0.0045400, 0.0047740, 0.0050640, 0.0053990, 0.0057960, 0.0062140, 0.0066710, 0.0071670, 0.0077360, 0.0083510, 0.0090350, 0.0097700, 0.0105670, 0.0113980, 0.0122910, 0.0132240, 0.0142670, 0.0153530, 0.0164840, 0.0176170, 0.0187590, 0.0199140, 0.0211040, 0.0224230, 0.0238470, 0.0253570, 0.0270500, 0.0289700, 0.0311880, 0.0337540, 0.0367470, 0.0405630, 0.0443080, 0.0484980, 0.0532290, 0.0587780, 0.0646170, 0.0709470, 0.0778340, 0.0856860, 0.0948090, 0.1050900, 0.1165920, 0.1293060, 0.1427320, 0.1576380, 0.1744580, 0.1930270, 0.2129300, 0.2326570, 0.2518260, 0.2709430, 0.2897560, 0.3079980, 0.3253930, 0.3416620, 0.3587460, 0.3766830, 0.3955170, 0.4152930, 0.4360580, 0.4578600, 0.4807530, 0.5047910, 0.5300310, 0.5565320, 0.5843590, 0.6135770, 0.6442560, 0.6764680, 0.7102920, 0.7458060, 0.7830970, 0.8222510, 0.8633640, 0.9065320]
	\( q_x \) for males as recorded in the 2021 period life table for the US Social Security Administration.
real(kind=rk), dimension(0:119), parameter, public	usss_f_qx_dat = [ 0.0050630, 0.0003930, 0.0002230, 0.0001770, 0.0001440, 0.0001220, 0.0001090, 0.0001020, 0.0000980, 0.0000970, 0.0001030, 0.0001130, 0.0001310, 0.0001570, 0.0001900, 0.0002330, 0.0002910, 0.0003550, 0.0004180, 0.0004610, 0.0005070, 0.0005560, 0.0006100, 0.0006660, 0.0007220, 0.0007750, 0.0008310, 0.0008890, 0.0009520, 0.0010250, 0.0011040, 0.0011920, 0.0012890, 0.0013830, 0.0014650, 0.0015440, 0.0016260, 0.0017190, 0.0018240, 0.0019400, 0.0020660, 0.0022020, 0.0023510, 0.0024820, 0.0026220, 0.0027890, 0.0029940, 0.0032190, 0.0034670, 0.0037290, 0.0040110, 0.0043060, 0.0046340, 0.0049810, 0.0053700, 0.0058310, 0.0063260, 0.0068370, 0.0073990, 0.0080330, 0.0086870, 0.0094110, 0.0101390, 0.0108490, 0.0115500, 0.0122160, 0.0129520, 0.0138440, 0.0148630, 0.0160280, 0.0173290, 0.0188590, 0.0206090, 0.0226200, 0.0249580, 0.0279060, 0.0309250, 0.0341400, 0.0376200, 0.0417250, 0.0463240, 0.0513340, 0.0569110, 0.0632790, 0.0707040, 0.0791840, 0.0886970, 0.0992400, 0.1104800, 0.1230780, 0.1371520, 0.1526050, 0.1694940, 0.1876230, 0.2066470, 0.2258900, 0.2450540, 0.2638150, 0.2818280, 0.2987380, 0.3166620, 0.3356620, 0.3558020, 0.3771500, 0.3997790, 0.4237660, 0.4491920, 0.4761430, 0.5047120, 0.5349940, 0.5670940, 0.6011200, 0.6371870, 0.6754180, 0.7102920, 0.7458060, 0.7830970, 0.8222510, 0.8633640, 0.9065320]
	\( q_x \) for females as recorded in the 2021 period life table for the US Social Security Administration.
real(kind=rk), dimension(0:100), parameter, public	uscdc_w_f_lx_dat = [ 100000, 99594, 99565, 99547, 99536, 99526, 99517, 99509, 99501, 99494, 99487, 99480, 99472, 99463, 99450, 99433, 99410, 99383, 99351, 99314, 99273, 99227, 99176, 99120, 99059, 98992, 98920, 98843, 98759, 98667, 98566, 98457, 98339, 98212, 98077, 97933, 97781, 97619, 97447, 97265, 97074, 96871, 96655, 96426, 96185, 95929, 95658, 95368, 95057, 94725, 94371, 93996, 93596, 93169, 92709, 92213, 91680, 91110, 90497, 89837, 89127, 88364, 87548, 86684, 85779, 84833, 83844, 82800, 81693, 80509, 79235, 77876, 76421, 74863, 73179, 71381, 69377, 67214, 64874, 62393, 59748, 56950, 54018, 50925, 47681, 44270, 40716, 37095, 33384, 29635, 25909, 22273, 18795, 15540, 12566, 9919, 7628, 5706, 4143, 2915, 1985]
	\( l_x \) from National Vital Statistics Reports, Volume 72, Number 12, United States Life Tables, 2021, White Females
real(kind=rk), dimension(0:100), parameter, public	uscdc_w_m_lx_dat = [ 100000, 99532, 99493, 99466, 99443, 99426, 99411, 99397, 99384, 99373, 99363, 99353, 99342, 99327, 99304, 99270, 99225, 99168, 99099, 99016, 98921, 98812, 98689, 98552, 98402, 98239, 98066, 97880, 97682, 97470, 97246, 97008, 96757, 96495, 96223, 95942, 95652, 95351, 95041, 94719, 94385, 94038, 93675, 93296, 92902, 92492, 92062, 91608, 91124, 90609, 90060, 89478, 88860, 88199, 87490, 86725, 85903, 85026, 84088, 83084, 82013, 80874, 79670, 78407, 77091, 75722, 74301, 72810, 71249, 69611, 67896, 66113, 64254, 62304, 60243, 58093, 55744, 53282, 50670, 47963, 45115, 42200, 39199, 36136, 33021, 29850, 26717, 23576, 20479, 17483, 14643, 12011, 9630, 7534, 5740, 4252, 3056, 2129, 1434, 934, 587]
	\( l_x \) from National Vital Statistics Reports, Volume 72, Number 12, United States Life Tables, 2021, White Males
real(kind=rk), dimension(0:100), parameter, public	uscdc_w_lx_dat = [ 100000, 99562, 99527, 99505, 99488, 99475, 99463, 99451, 99441, 99432, 99423, 99415, 99406, 99393, 99375, 99349, 99315, 99273, 99221, 99161, 99092, 99014, 98926, 98828, 98721, 98606, 98482, 98349, 98206, 98053, 97889, 97714, 97528, 97333, 97128, 96914, 96691, 96458, 96215, 95962, 95697, 95420, 95128, 94822, 94502, 94167, 93814, 93439, 93039, 92613, 92158, 91675, 91162, 90613, 90024, 89388, 88706, 87978, 87197, 86360, 85464, 84506, 83490, 82419, 81301, 80137, 78925, 77650, 76310, 74893, 73392, 71814, 70151, 68390, 66512, 64531, 62348, 60029, 57547, 54948, 52197, 49338, 46371, 43294, 40117, 36832, 33508, 30123, 26725, 23367, 20105, 16996, 14093, 11443, 9082, 7035, 5308, 3895, 2775, 1918, 1283]
	\( l_x \) from National Vital Statistics Reports, Volume 72, Number 12, United States Life Tables, 2021, White
real(kind=rk), dimension(0:100), parameter, public	uscdc_lx_dat = [ 100000, 99455, 99415, 99390, 99371, 99355, 99341, 99328, 99316, 99305, 99296, 99287, 99277, 99264, 99243, 99214, 99173, 99123, 99061, 98988, 98906, 98812, 98706, 98591, 98467, 98335, 98197, 98052, 97899, 97737, 97566, 97386, 97196, 96998, 96792, 96577, 96354, 96122, 95880, 95627, 95363, 95084, 94792, 94484, 94162, 93824, 93468, 93091, 92690, 92261, 91803, 91316, 90797, 90241, 89644, 89000, 88309, 87570, 86778, 85928, 85017, 84042, 83005, 81912, 80767, 79571, 78325, 77015, 75640, 74193, 72671, 71078, 69405, 67644, 65776, 63810, 61658, 59380, 56945, 54396, 51702, 48904, 45995, 42987, 39882, 36667, 33399, 30073, 26734, 23433, 20222, 17157, 14288, 11660, 9310, 7260, 5520, 4086, 2940, 2053, 1390]
	\( l_x \) from National Vital Statistics Reports, Volume 72, Number 12, United States Life Tables, 2021

Detailed Description

Life table computations, and some US life table data.

Life Table Data

The following tables are provided as public arrays exported from this module:

• \( l_x \) for males as recorded in the 2021 period life table for the US Social Security Administration.
• \( l_x \) for females as recorded in the 2021 period life table for the US Social Security Administration.
• \( q_x \) for males as recorded in the 2021 period life table for the US Social Security Administration.
• \( q_x \) for females as recorded in the 2021 period life table for the US Social Security Administration.
• \( l_x \) from National Vital Statistics Reports, Volume 72, Number 12, United States Life Tables, 2021, White Females
• \( l_x \) from National Vital Statistics Reports, Volume 72, Number 12, United States Life Tables, 2021, White Males
• \( l_x \) from National Vital Statistics Reports, Volume 72, Number 12, United States Life Tables, 2021, White
• \( l_x \) from National Vital Statistics Reports, Volume 72, Number 12, United States Life Tables, 2021

Computation

probability_of_death

\( q_x \) is the probability that someone aged exactly \( x \) will die before reaching age \( (x+1) \).

\[ q_x = 1 - \frac{l_{x+1}}{l_x} \]

Warning

It is common for the value of \( q_x \) to be adjusted. It is also common for life tables with adjusted \( q_x \) values to still report the actual values for \( l_x \) – thus making the two columns inconsistent with each other with respect to the above formula. The 2021 Social Security life table is an example. This module treats this single life table as two separate, and independent entities – this allows us to use whichever column is most appropriate for our application.

probability_of_survival_1

\( p_x \) is the probability that someone aged exactly \( x \) will survive to age \( (x+1) \).

\[ p_x = 1 - q_x \]

\[ p_x = \frac{l_{x+1}}{l_x} \]

cohort_size

\( l_0 \) is the number of people in the cohort (sometimes called the "radix").

survivors & age_all_dead

\( l_x \) is the number of people who survive to age \( x \).

\[ l_x = (1 - q_x)l_{x-1} \text{ with } l_0 \text{ known}\]

died

\( d_x \) is the number of people who die aged \( x \) – i.e. last birthday was age \( x \).

\[ d_x = l_x q_x \]

\[ d_x = l_x - l_{x+1} \]

probability_of_survival_n

\( _tp_x \) the probability that someone aged exactly \( x \) will survive for \( t \) more years living up to at least age \( x+t \).

\[ _tp_x = \frac{l_{x+t}}{l_x} \]

person_years

\( L_x \) the total number of person-years lived by the cohort from age \( x \) to \( x+1 \).

\[ L_x = l_{x+1} + \frac{d_x}{2} \]

Warning

I like the simple approach of assuming people die uniformly on the time interval. That is to say the average number of years lived by people who died on the interval was 0.5 years. There are several other methodologies in common use today that do not make this assumption. The most common approaches are to use some kind of smoothing criteria. For a popular example, see "Keyfitz N. A life table that agrees with the data. Journal of the American Statistical Association. 1966 Jun 1".

total_person_years

\( T_x \) the total number of person-years lived by the cohort from age \( x \) until all have died.

\[ T_x = \sum_{k=x}^\infty L_k \]

life_expectancy & life_expectancy_at_birth

\( e_x \) is the average number of years of life remaining at age \( x \). This value is provided directly in our data table, so we do not use the approximation below.

\[ e_x = \frac{T_x}{l_x} \]

mortality_rate

\( m_x \) is the mortality rate at age \( x \).

\[ m_x = \frac{d_x}{L_x} \]

life_table & cohort parameters

Every function in this library takes life_table and cohort_size as the last two arguments. These arguments are used in the same way in all functions, and are documented here:

• life_table is a rank 1 array containing life table data enumerated at whole number ages starting at 0 and incrementing by one for each element. It may contain values for the survival function (number of people alive at the given age) or the probability_of_death function (the probability of someone at a given age expiring within one year). The upper and lower bounds are irrelevant; however, it is very important that the first element of the array express the value for the function at age 0. I normally use a lower bound of zero.
• cohort_size is used to identify the type of functional data stored in life_table, and to specify the cohort size when that functional data is the probability_of_death. When cohort_size <= 0 the life_table is assumed to contain the survival function (in this case the cohort size is the first element of the life_table array). When cohort_size > 0, the life_table is assumed to contain the probability of death function and the value of cohort_size is used to compute the survival function at age 0 - i.e. it is used as the cohort size.

Function/Subroutine Documentation

survivors()

real(kind=rk) pure function, public mrffl_life_table::survivors	(	integer(kind=ik), intent(in)	age,
		real(kind=rk), dimension(:), intent(in)	life_table,
		integer(kind=ik), intent(in)	cohort_size )

Return \( l_x \) for the given age.

See the module documentation for a guide to symbols.

Parameters

age	Age of the person.
life_table	Data for life table. See module documentation for description.
cohort_size	Number of people in the cohort. See module documentation for description.

Definition at line 280 of file mrffl_life_table.f90.

References survivors().

Referenced by age_all_dead(), died(), life_expectancy(), life_table_print(), person_years(), probability_of_survival_n(), rand_age(), and survivors().

Here is the call graph for this function:

Here is the caller graph for this function:

probability_of_death()

real(kind=rk) pure function, public mrffl_life_table::probability_of_death	(	integer(kind=ik), intent(in)	age,
		real(kind=rk), dimension(:), intent(in)	life_table,
		integer(kind=ik), intent(in)	cohort_size )

Return \( q_x \) for the given age.

See the module documentation for a guide to symbols.

Parameters

age	Age of the person.
life_table	Data for life table. See module documentation for description.
cohort_size	Number of people in the cohort. See module documentation for description.

Definition at line 314 of file mrffl_life_table.f90.

References probability_of_death(), and mrffl_config::zero_epsilon.

Referenced by life_table_print(), and probability_of_death().

Here is the call graph for this function:

Here is the caller graph for this function:

life_expectancy()

real(kind=rk) pure function, public mrffl_life_table::life_expectancy	(	integer(kind=ik), intent(in)	age,
		real(kind=rk), dimension(:), intent(in)	life_table,
		integer(kind=ik), intent(in)	cohort_size )

Return \( e_x \) for the given age.

See the module documentation for a guide to symbols.

Parameters

age	Age of the person.
life_table	Data for life table. See module documentation for description.
cohort_size	Number of people in the cohort. See module documentation for description.

Definition at line 348 of file mrffl_life_table.f90.

References life_expectancy(), survivors(), total_person_years(), and mrffl_config::zero_epsilon.

Referenced by life_expectancy(), life_expectancy_at_birth(), and life_table_print().

Here is the call graph for this function:

Here is the caller graph for this function:

life_expectancy_at_birth()

real(kind=rk) pure function, public mrffl_life_table::life_expectancy_at_birth	(	real(kind=rk), dimension(:), intent(in)	life_table,
		integer(kind=ik), intent(in)	cohort_size )

Return \( e_0 \).

See the module documentation for a guide to symbols.

Parameters

life_table	Data for life table. See module documentation for description.
cohort_size	Number of people in the cohort. See module documentation for description.

Definition at line 367 of file mrffl_life_table.f90.

References life_expectancy(), and life_expectancy_at_birth().

Referenced by life_expectancy_at_birth().

Here is the call graph for this function:

Here is the caller graph for this function:

probability_of_survival_n()

real(kind=rk) pure function, public mrffl_life_table::probability_of_survival_n	(	integer(kind=ik), intent(in)	age,
		integer(kind=ik), intent(in)	n,
		real(kind=rk), dimension(:), intent(in)	life_table,
		integer(kind=ik), intent(in)	cohort_size )

Return \( _tp_x \) for the given age.

See the module documentation for a guide to symbols.

Parameters

age	Age of the person.
n	Number of years. Must be non-negative.
life_table	Data for life table. See module documentation for description.
cohort_size	Number of people in the cohort. See module documentation for description.

Definition at line 382 of file mrffl_life_table.f90.

References probability_of_survival_n(), survivors(), and mrffl_config::zero_epsilon.

Referenced by probability_of_survival_1(), and probability_of_survival_n().

Here is the call graph for this function:

Here is the caller graph for this function:

probability_of_survival_1()

real(kind=rk) pure function, public mrffl_life_table::probability_of_survival_1	(	integer(kind=ik), intent(in)	age,
		real(kind=rk), dimension(:), intent(in)	life_table,
		integer(kind=ik), intent(in)	cohort_size )

Return \( p_x \) for the given age.

See the module documentation for a guide to symbols.

Parameters

age	Age of the person.
life_table	Data for life table. See module documentation for description.
cohort_size	Number of people in the cohort. See module documentation for description.

Definition at line 402 of file mrffl_life_table.f90.

References probability_of_survival_1(), and probability_of_survival_n().

Referenced by life_table_print(), and probability_of_survival_1().

Here is the call graph for this function:

Here is the caller graph for this function:

died()

real(kind=rk) pure function, public mrffl_life_table::died	(	integer(kind=ik), intent(in)	age,
		real(kind=rk), dimension(:), intent(in)	life_table,
		integer(kind=ik), intent(in)	cohort_size )

Return \( d_x \) for the given age.

See the module documentation for a guide to symbols.

Parameters

age	Age of the person.
life_table	Data for life table. See module documentation for description.
cohort_size	Number of people in the cohort. See module documentation for description.

Definition at line 416 of file mrffl_life_table.f90.

References died(), and survivors().

Referenced by died(), life_table_print(), and mortality_rate().

Here is the call graph for this function:

Here is the caller graph for this function:

person_years()

real(kind=rk) pure function, public mrffl_life_table::person_years	(	integer(kind=ik), intent(in)	age,
		real(kind=rk), dimension(:), intent(in)	life_table,
		integer(kind=ik), intent(in)	cohort_size )

Return \( L_x \) for the given age.

See the module documentation for a guide to symbols.

Parameters

age	Age of the person.
life_table	Data for life table. See module documentation for description.
cohort_size	Number of people in the cohort. See module documentation for description.

Definition at line 430 of file mrffl_life_table.f90.

References person_years(), and survivors().

Referenced by life_table_print(), mortality_rate(), person_years(), and total_person_years().

Here is the call graph for this function:

Here is the caller graph for this function:

total_person_years()

real(kind=rk) pure function, public mrffl_life_table::total_person_years	(	integer(kind=ik), intent(in)	age,
		real(kind=rk), dimension(:), intent(in)	life_table,
		integer(kind=ik), intent(in)	cohort_size )

Return \( T_x \) for the given age.

See the module documentation for a guide to symbols.

Parameters

age	Age of the person.
life_table	Data for life table. See module documentation for description.
cohort_size	Number of people in the cohort. See module documentation for description.

Definition at line 447 of file mrffl_life_table.f90.

References person_years(), and total_person_years().

Referenced by life_expectancy(), life_table_print(), and total_person_years().

Here is the call graph for this function:

Here is the caller graph for this function:

mortality_rate()

real(kind=rk) pure function, public mrffl_life_table::mortality_rate	(	integer(kind=ik), intent(in)	age,
		real(kind=rk), dimension(:), intent(in)	life_table,
		integer(kind=ik), intent(in)	cohort_size )

Return \( m_x \) for the given age.

See the module documentation for a guide to symbols.

Parameters

age	Age of the person.
life_table	Data for life table. See module documentation for description.
cohort_size	Number of people in the cohort. See module documentation for description.

Definition at line 465 of file mrffl_life_table.f90.

References died(), mortality_rate(), person_years(), and mrffl_config::zero_epsilon.

Referenced by life_table_print(), and mortality_rate().

Here is the call graph for this function:

Here is the caller graph for this function:

age_all_dead()

real(kind=rk) pure function, public mrffl_life_table::age_all_dead	(	real(kind=rk), dimension(:), intent(in)	life_table,
		integer(kind=ik), intent(in)	cohort_size )

Return lowest age for which \( l_x=0 \).

See the module documentation for a guide to symbols.

This function is super slow.

Parameters

life_table	Data for life table. See module documentation for description.
cohort_size	Number of people in the cohort. See module documentation for description.

Definition at line 486 of file mrffl_life_table.f90.

References age_all_dead(), survivors(), and mrffl_config::zero_epsilon.

Referenced by age_all_dead().

Here is the call graph for this function:

Here is the caller graph for this function:

rand_age()

integer(kind=ik) function, public mrffl_life_table::rand_age	(	integer(kind=ik), intent(in)	age,
		real(kind=rk), dimension(:), intent(in)	life_table,
		integer(kind=ik), intent(in)	cohort_size )

Return random age for death given current age and life_table.

This function is super slow.

Parameters

age	Age of the person.
life_table	Data for life table. See module documentation for description.
cohort_size	Number of people in the cohort. See module documentation for description.

Definition at line 509 of file mrffl_life_table.f90.

References rand_age(), mrffl_stats::rand_int(), and survivors().

Referenced by rand_age().

Here is the call graph for this function:

Here is the caller graph for this function:

life_table_print()

subroutine, public mrffl_life_table::life_table_print	(	integer, intent(in)	out_io_unit,
		integer(kind=ik), intent(in)	print_out,
		real(kind=rk), dimension(:), intent(in)	life_table,
		integer(kind=ik), intent(in)	cohort_size )

Print life table.

An ERROR STOP occures if a WRITE causes an I/O error

Parameters

out_io_unit	Unit to which to print table
print_out	Bitset built from the following constants prt_title, prt_table, & prt_space
life_table	Data for life table. See module documentation for description.
cohort_size	Number of people in the cohort. See module documentation for description.

Definition at line 534 of file mrffl_life_table.f90.

References mrffl_bitset::bitset_subsetp(), died(), life_expectancy(), mortality_rate(), person_years(), probability_of_death(), probability_of_survival_1(), mrffl_prt_sets::prt_space, mrffl_prt_sets::prt_table, mrffl_prt_sets::prt_title, survivors(), and total_person_years().

Here is the call graph for this function:

Variable Documentation

usss_m_lx_dat

real(kind=rk), dimension(0:119), parameter, public mrffl_life_table::usss_m_lx_dat = [ 100000, 99414, 99372, 99345, 99323, 99304, 99289, 99275, 99262, 99250, 99238, 99225, 99211, 99195, 99173, 99143, 99098, 99035, 98949, 98840, 98715, 98579, 98433, 98275, 98106, 97926, 97734, 97530, 97316, 97089, 96850, 96601, 96342, 96073, 95797, 95512, 95218, 94916, 94603, 94277, 93937, 93582, 93211, 92825, 92423, 92003, 91564, 91100, 90608, 90083, 89523, 88926, 88289, 87606, 86874, 86089, 85248, 84347, 83386, 82361, 81272, 80112, 78882, 77582, 76215, 74786, 73296, 71749, 70141, 68468, 66732, 64927, 63046, 61080, 59018, 56849, 54543, 52126, 49598, 46958, 44198, 41342, 38409, 35420, 32385, 29314, 26234, 23175, 20178, 17298, 14571, 12029, 9707, 7640, 5863, 4386, 3198, 2271, 1572, 1060, 698, 448, 279, 169, 99, 56, 30, 16, 8, 4, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0]

\( l_x \) for males as recorded in the 2021 period life table for the US Social Security Administration.

Definition at line 134 of file mrffl_life_table.f90.

usss_f_lx_dat

real(kind=rk), dimension(0:119), parameter, public mrffl_life_table::usss_f_lx_dat = [ 100000, 99494, 99455, 99432, 99415, 99400, 99388, 99378, 99367, 99358, 99348, 99338, 99327, 99314, 99298, 99279, 99256, 99227, 99192, 99150, 99105, 99055, 98999, 98939, 98873, 98802, 98725, 98643, 98555, 98462, 98361, 98252, 98135, 98008, 97873, 97730, 97579, 97420, 97252, 97075, 96887, 96687, 96474, 96247, 96008, 95756, 95489, 95203, 94897, 94568, 94215, 93837, 93433, 93000, 92537, 92040, 91503, 90924, 90303, 89635, 88915, 88142, 87313, 86427, 85490, 84502, 83470, 82389, 81248, 80041, 78758, 77393, 75934, 74369, 72686, 70872, 68895, 66764, 64485, 62059, 59469, 56714, 53803, 50741, 47530, 44170, 40672, 37065, 33386, 29698, 26043, 22471, 19042, 15814, 12847, 10192, 7890, 5956, 4385, 3149, 2208, 1509, 1003, 646, 402, 241, 139, 77, 40, 20, 9, 4, 2, 1, 0, 0, 0, 0, 0, 0]

\( l_x \) for females as recorded in the 2021 period life table for the US Social Security Administration.

Definition at line 151 of file mrffl_life_table.f90.

usss_m_qx_dat

real(kind=rk), dimension(0:119), parameter, public mrffl_life_table::usss_m_qx_dat = [ 0.0058600, 0.0004200, 0.0002720, 0.0002250, 0.0001840, 0.0001570, 0.0001400, 0.0001280, 0.0001220, 0.0001230, 0.0001290, 0.0001380, 0.0001640, 0.0002200, 0.0003100, 0.0004460, 0.0006370, 0.0008680, 0.0011000, 0.0012700, 0.0013730, 0.0014880, 0.0016050, 0.0017140, 0.0018350, 0.0019630, 0.0020820, 0.0022020, 0.0023300, 0.0024570, 0.0025740, 0.0026830, 0.0027870, 0.0028810, 0.0029740, 0.0030740, 0.0031750, 0.0032950, 0.0034440, 0.0036080, 0.0037800, 0.0039580, 0.0041440, 0.0043370, 0.0045400, 0.0047740, 0.0050640, 0.0053990, 0.0057960, 0.0062140, 0.0066710, 0.0071670, 0.0077360, 0.0083510, 0.0090350, 0.0097700, 0.0105670, 0.0113980, 0.0122910, 0.0132240, 0.0142670, 0.0153530, 0.0164840, 0.0176170, 0.0187590, 0.0199140, 0.0211040, 0.0224230, 0.0238470, 0.0253570, 0.0270500, 0.0289700, 0.0311880, 0.0337540, 0.0367470, 0.0405630, 0.0443080, 0.0484980, 0.0532290, 0.0587780, 0.0646170, 0.0709470, 0.0778340, 0.0856860, 0.0948090, 0.1050900, 0.1165920, 0.1293060, 0.1427320, 0.1576380, 0.1744580, 0.1930270, 0.2129300, 0.2326570, 0.2518260, 0.2709430, 0.2897560, 0.3079980, 0.3253930, 0.3416620, 0.3587460, 0.3766830, 0.3955170, 0.4152930, 0.4360580, 0.4578600, 0.4807530, 0.5047910, 0.5300310, 0.5565320, 0.5843590, 0.6135770, 0.6442560, 0.6764680, 0.7102920, 0.7458060, 0.7830970, 0.8222510, 0.8633640, 0.9065320]

\( q_x \) for males as recorded in the 2021 period life table for the US Social Security Administration.

cohort_size=100000

Definition at line 169 of file mrffl_life_table.f90.

usss_f_qx_dat

real(kind=rk), dimension(0:119), parameter, public mrffl_life_table::usss_f_qx_dat = [ 0.0050630, 0.0003930, 0.0002230, 0.0001770, 0.0001440, 0.0001220, 0.0001090, 0.0001020, 0.0000980, 0.0000970, 0.0001030, 0.0001130, 0.0001310, 0.0001570, 0.0001900, 0.0002330, 0.0002910, 0.0003550, 0.0004180, 0.0004610, 0.0005070, 0.0005560, 0.0006100, 0.0006660, 0.0007220, 0.0007750, 0.0008310, 0.0008890, 0.0009520, 0.0010250, 0.0011040, 0.0011920, 0.0012890, 0.0013830, 0.0014650, 0.0015440, 0.0016260, 0.0017190, 0.0018240, 0.0019400, 0.0020660, 0.0022020, 0.0023510, 0.0024820, 0.0026220, 0.0027890, 0.0029940, 0.0032190, 0.0034670, 0.0037290, 0.0040110, 0.0043060, 0.0046340, 0.0049810, 0.0053700, 0.0058310, 0.0063260, 0.0068370, 0.0073990, 0.0080330, 0.0086870, 0.0094110, 0.0101390, 0.0108490, 0.0115500, 0.0122160, 0.0129520, 0.0138440, 0.0148630, 0.0160280, 0.0173290, 0.0188590, 0.0206090, 0.0226200, 0.0249580, 0.0279060, 0.0309250, 0.0341400, 0.0376200, 0.0417250, 0.0463240, 0.0513340, 0.0569110, 0.0632790, 0.0707040, 0.0791840, 0.0886970, 0.0992400, 0.1104800, 0.1230780, 0.1371520, 0.1526050, 0.1694940, 0.1876230, 0.2066470, 0.2258900, 0.2450540, 0.2638150, 0.2818280, 0.2987380, 0.3166620, 0.3356620, 0.3558020, 0.3771500, 0.3997790, 0.4237660, 0.4491920, 0.4761430, 0.5047120, 0.5349940, 0.5670940, 0.6011200, 0.6371870, 0.6754180, 0.7102920, 0.7458060, 0.7830970, 0.8222510, 0.8633640, 0.9065320]

\( q_x \) for females as recorded in the 2021 period life table for the US Social Security Administration.

cohort_size=100000

Definition at line 187 of file mrffl_life_table.f90.

uscdc_w_f_lx_dat

real(kind=rk), dimension(0:100), parameter, public mrffl_life_table::uscdc_w_f_lx_dat = [ 100000, 99594, 99565, 99547, 99536, 99526, 99517, 99509, 99501, 99494, 99487, 99480, 99472, 99463, 99450, 99433, 99410, 99383, 99351, 99314, 99273, 99227, 99176, 99120, 99059, 98992, 98920, 98843, 98759, 98667, 98566, 98457, 98339, 98212, 98077, 97933, 97781, 97619, 97447, 97265, 97074, 96871, 96655, 96426, 96185, 95929, 95658, 95368, 95057, 94725, 94371, 93996, 93596, 93169, 92709, 92213, 91680, 91110, 90497, 89837, 89127, 88364, 87548, 86684, 85779, 84833, 83844, 82800, 81693, 80509, 79235, 77876, 76421, 74863, 73179, 71381, 69377, 67214, 64874, 62393, 59748, 56950, 54018, 50925, 47681, 44270, 40716, 37095, 33384, 29635, 25909, 22273, 18795, 15540, 12566, 9919, 7628, 5706, 4143, 2915, 1985]

\( l_x \) from National Vital Statistics Reports, Volume 72, Number 12, United States Life Tables, 2021, White Females

Definition at line 204 of file mrffl_life_table.f90.

uscdc_w_m_lx_dat

real(kind=rk), dimension(0:100), parameter, public mrffl_life_table::uscdc_w_m_lx_dat = [ 100000, 99532, 99493, 99466, 99443, 99426, 99411, 99397, 99384, 99373, 99363, 99353, 99342, 99327, 99304, 99270, 99225, 99168, 99099, 99016, 98921, 98812, 98689, 98552, 98402, 98239, 98066, 97880, 97682, 97470, 97246, 97008, 96757, 96495, 96223, 95942, 95652, 95351, 95041, 94719, 94385, 94038, 93675, 93296, 92902, 92492, 92062, 91608, 91124, 90609, 90060, 89478, 88860, 88199, 87490, 86725, 85903, 85026, 84088, 83084, 82013, 80874, 79670, 78407, 77091, 75722, 74301, 72810, 71249, 69611, 67896, 66113, 64254, 62304, 60243, 58093, 55744, 53282, 50670, 47963, 45115, 42200, 39199, 36136, 33021, 29850, 26717, 23576, 20479, 17483, 14643, 12011, 9630, 7534, 5740, 4252, 3056, 2129, 1434, 934, 587]

\( l_x \) from National Vital Statistics Reports, Volume 72, Number 12, United States Life Tables, 2021, White Males

Definition at line 220 of file mrffl_life_table.f90.

uscdc_w_lx_dat

real(kind=rk), dimension(0:100), parameter, public mrffl_life_table::uscdc_w_lx_dat = [ 100000, 99562, 99527, 99505, 99488, 99475, 99463, 99451, 99441, 99432, 99423, 99415, 99406, 99393, 99375, 99349, 99315, 99273, 99221, 99161, 99092, 99014, 98926, 98828, 98721, 98606, 98482, 98349, 98206, 98053, 97889, 97714, 97528, 97333, 97128, 96914, 96691, 96458, 96215, 95962, 95697, 95420, 95128, 94822, 94502, 94167, 93814, 93439, 93039, 92613, 92158, 91675, 91162, 90613, 90024, 89388, 88706, 87978, 87197, 86360, 85464, 84506, 83490, 82419, 81301, 80137, 78925, 77650, 76310, 74893, 73392, 71814, 70151, 68390, 66512, 64531, 62348, 60029, 57547, 54948, 52197, 49338, 46371, 43294, 40117, 36832, 33508, 30123, 26725, 23367, 20105, 16996, 14093, 11443, 9082, 7035, 5308, 3895, 2775, 1918, 1283]

\( l_x \) from National Vital Statistics Reports, Volume 72, Number 12, United States Life Tables, 2021, White

Definition at line 236 of file mrffl_life_table.f90.

uscdc_lx_dat

real(kind=rk), dimension(0:100), parameter, public mrffl_life_table::uscdc_lx_dat = [ 100000, 99455, 99415, 99390, 99371, 99355, 99341, 99328, 99316, 99305, 99296, 99287, 99277, 99264, 99243, 99214, 99173, 99123, 99061, 98988, 98906, 98812, 98706, 98591, 98467, 98335, 98197, 98052, 97899, 97737, 97566, 97386, 97196, 96998, 96792, 96577, 96354, 96122, 95880, 95627, 95363, 95084, 94792, 94484, 94162, 93824, 93468, 93091, 92690, 92261, 91803, 91316, 90797, 90241, 89644, 89000, 88309, 87570, 86778, 85928, 85017, 84042, 83005, 81912, 80767, 79571, 78325, 77015, 75640, 74193, 72671, 71078, 69405, 67644, 65776, 63810, 61658, 59380, 56945, 54396, 51702, 48904, 45995, 42987, 39882, 36667, 33399, 30073, 26734, 23433, 20222, 17157, 14288, 11660, 9310, 7260, 5520, 4086, 2940, 2053, 1390]

\( l_x \) from National Vital Statistics Reports, Volume 72, Number 12, United States Life Tables, 2021

Definition at line 252 of file mrffl_life_table.f90.