mrffl_stats Module Reference

Some statstical utilities supporting other MRFFL modules. More...

Functions/Subroutines
integer(kind=ik) function, public	rand_int (upper_bound, optional_lower_bound)
	Return random integer in U([optional_lower_bound,upper_bound)) – optional_lower_bound is 0 if missing.
real(kind=rk) function, public	rand_real (upper_bound, optional_lower_bound)
	Return random real value in U([optional_lower_bound,upper_bound)) – optional_lower_bound is 0 if missing.
real(kind=rk) function, public	resample_tail (data, tail_length)
	Return random value from among the last tail_length elements of data.
real(kind=rk) function, public	resample_head (data, head_length)
	Return random value from among the first head_length elements of data.
subroutine, public	mean_and_variance (mean, variance, data)
	Return mean & variance of elements in an array.
real(kind=rk) function, public	rand_norm_std ()
	Return random value from the standard normal distribution.
real(kind=rk) function, public	rand_norm_std_box ()
	Return random value from the standard normal distribution using the Box-Muller transform.
real(kind=rk) function, public	rand_norm_std_probit_clip ()
	Return random value from the standard normal distribution in [-5.612, 5.612] using the Probit function.
real(kind=rk) function, public	rand_norm_std_probit ()
	Return random value from the standard normal distribution using the Probit function.
real(kind=rk) function, public	rand_norm (mean, variance)
	Return random value from the specified normal distribution.
real(kind=rk) function, public	rand_log_norm (mu, sigma)
	Return random value from the specified log-normal distribution.
real(kind=rk) function, public	probit (p)
	Probit function – i.e.
real(kind=rk) function	poly_eval (p, x)
	Evaluate a univariate polynomial.
subroutine, public	geometric_brownian_motion (step_values, s0, mu, sigma)
	Compute a set of random steps in a GBM process.
subroutine, public	zero_clipped_brownian_motion (step_values, s0, mu, sigma)
	Compute a set of random steps in a zero clipped browinan motion.

Detailed Description

Some statstical utilities supporting other MRFFL modules.

Function/Subroutine Documentation

rand_int()

integer(kind=ik) function, public mrffl_stats::rand_int	(	integer(kind=ik), intent(in)	upper_bound,
		integer(kind=ik), intent(in), optional	optional_lower_bound )

Return random integer in U([optional_lower_bound,upper_bound)) – optional_lower_bound is 0 if missing.

Parameters

upper_bound	Upper bound for random number
optional_lower_bound	Lower bound for random number

Definition at line 62 of file mrffl_stats.f90.

References rand_int().

Referenced by mrffl_life_table::rand_age(), rand_int(), resample_head(), and resample_tail().

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rand_real()

real(kind=rk) function, public mrffl_stats::rand_real	(	real(kind=rk), intent(in)	upper_bound,
		real(kind=rk), intent(in), optional	optional_lower_bound )

Return random real value in U([optional_lower_bound,upper_bound)) – optional_lower_bound is 0 if missing.

Parameters

upper_bound	Upper bound for random number
optional_lower_bound	Lower bound for random number

Definition at line 82 of file mrffl_stats.f90.

References rand_real().

Referenced by rand_real().

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resample_tail()

real(kind=rk) function, public mrffl_stats::resample_tail	(	real(kind=rk), dimension(:), intent(in)	data,
		integer(kind=ik), intent(in)	tail_length )

Return random value from among the last tail_length elements of data.

Parameters

data	The data set – a rank 1 array.
tail_length	Number of elements to consider for resample.

Definition at line 102 of file mrffl_stats.f90.

References rand_int(), and resample_tail().

Referenced by mrffl_us_markets::dgs10_resample(), mrffl_us_markets::dow_resample(), mrffl_us_inflation::inf_resample(), mrffl_us_markets::nas_resample(), resample_tail(), mrffl_us_markets::rut_resample(), and mrffl_us_markets::snp_resample().

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resample_head()

real(kind=rk) function, public mrffl_stats::resample_head	(	real(kind=rk), dimension(:), intent(in)	data,
		integer(kind=ik), intent(in)	head_length )

Return random value from among the first head_length elements of data.

Parameters

data	The data set – a rank 1 array.
head_length	Number of elements to consider for resample.

Definition at line 119 of file mrffl_stats.f90.

References rand_int(), and resample_head().

Referenced by resample_head().

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mean_and_variance()

subroutine, public mrffl_stats::mean_and_variance	(	real(kind=rk), intent(out)	mean,
		real(kind=rk), intent(out)	variance,
		real(kind=rk), dimension(:), intent(in)	data )

Return mean & variance of elements in an array.

Parameters

mean	Holds the mean upon exit.
variance	Holds the variance (standard deviation squared) upon exit.
data	The data set – a rank 1 array.

Definition at line 137 of file mrffl_stats.f90.

rand_norm_std()

real(kind=rk) function, public mrffl_stats::rand_norm_std

Return random value from the standard normal distribution.

This function simply calls the preferred rand_norm_std_* function. Currently that's rand_norm_std_probit().

Definition at line 150 of file mrffl_stats.f90.

References rand_norm_std(), and rand_norm_std_probit().

Referenced by rand_log_norm(), rand_norm(), and rand_norm_std().

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rand_norm_std_box()

real(kind=rk) function, public mrffl_stats::rand_norm_std_box

Return random value from the standard normal distribution using the Box-Muller transform.

Reference: Box, G. E. P., and Mervin E. Muller. 1958. "A Note on the Generation of Random Normal Deviates." The Annals of Mathematical Statistics 29 (2): 610-11.

Definition at line 161 of file mrffl_stats.f90.

References rand_norm_std_box().

Referenced by rand_norm_std_box().

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rand_norm_std_probit_clip()

real(kind=rk) function, public mrffl_stats::rand_norm_std_probit_clip

Return random value from the standard normal distribution in [-5.612, 5.612] using the Probit function.

Definition at line 182 of file mrffl_stats.f90.

References probit(), rand_norm_std_probit_clip(), and mrffl_config::zero_epsilon.

Referenced by rand_norm_std_probit_clip().

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rand_norm_std_probit()

real(kind=rk) function, public mrffl_stats::rand_norm_std_probit

Return random value from the standard normal distribution using the Probit function.

Definition at line 197 of file mrffl_stats.f90.

References probit(), and rand_norm_std_probit().

Referenced by rand_norm_std(), and rand_norm_std_probit().

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rand_norm()

real(kind=rk) function, public mrffl_stats::rand_norm	(	real(kind=rk), intent(in)	mean,
		real(kind=rk), intent(in)	variance )

Return random value from the specified normal distribution.

Parameters

mean	Mean of the distribution
variance	Variance (standard deviation squared) of the distribution

Definition at line 215 of file mrffl_stats.f90.

References rand_norm(), and rand_norm_std().

Referenced by geometric_brownian_motion(), rand_norm(), and zero_clipped_brownian_motion().

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rand_log_norm()

real(kind=rk) function, public mrffl_stats::rand_log_norm	(	real(kind=rk), intent(in)	mu,
		real(kind=rk), intent(in)	sigma )

Return random value from the specified log-normal distribution.

\[ \text{mean} = e^\left(\mu+\frac{\sigma^2}{2}\right) \]

\[ \text{median} = e^\mu \]

\[ \text{variance} = \left[e^{\sigma^2}-1\right] e^{2\mu+\sigma^2} \]

Parameters

mu	Mean of the distribution
sigma	Standard deviation of the distribution

Definition at line 231 of file mrffl_stats.f90.

References rand_log_norm(), and rand_norm_std().

Referenced by rand_log_norm().

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probit()

real(kind=rk) function, public mrffl_stats::probit

(

real(kind=rk), intent(in)

p

)

Probit function – i.e.

inverse of standard normal CDF. Return $z_p$ such that \( P(\mathcal{N}(0, 1)<=z_p) = p \)

Reference: Wichura, Michael J. 1988. "Algorithm AS 241: The Percentage Points of the Normal Distribution." Journal of the Royal Statistical Society. Series C (Applied Statistics) 37 (3): 477-84.

Parameters

p	Probablity in \( (0,1) \).

Definition at line 246 of file mrffl_stats.f90.

References poly_eval(), and probit().

Referenced by probit(), rand_norm_std_probit(), and rand_norm_std_probit_clip().

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poly_eval()

real(kind=rk) function mrffl_stats::poly_eval ( real(kind=rk), dimension(:), intent(in) p, real(kind=rk), intent(in) x )

private

Evaluate a univariate polynomial.

Used by probit. Not exported from the module.

The polynomial is ordered in the natural way with the highest coefficient first in the array:

\[ p=\sum_{k=1}^{d+1} p_kx^{1+d-k} \]

Note that $k$ in the above formula is the index in the array p.

Parameters

p	A $d+1$ element, rank 1 array holding the coefficients of a polynomial
x	The value at which to evaluate the polynomial

Definition at line 315 of file mrffl_stats.f90.

References poly_eval().

Referenced by poly_eval(), and probit().

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geometric_brownian_motion()

subroutine, public mrffl_stats::geometric_brownian_motion	(	real(kind=rk), dimension(:), intent(out)	step_values,
		real(kind=rk), intent(in)	s0,
		real(kind=rk), intent(in)	mu,
		real(kind=rk), intent(in)	sigma )

Compute a set of random steps in a GBM process.

Parameters

s0	Initial value of an asset
mu	Mean gain for the assest over 1 unit of time
sigma	Standard deviation of gain for the assest over 1 unit of time
step_values	A rank 1 array which will hold the values of the asset over time

Definition at line 334 of file mrffl_stats.f90.

References rand_norm().

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zero_clipped_brownian_motion()

subroutine, public mrffl_stats::zero_clipped_brownian_motion	(	real(kind=rk), dimension(:), intent(out)	step_values,
		real(kind=rk), intent(in)	s0,
		real(kind=rk), intent(in)	mu,
		real(kind=rk), intent(in)	sigma )

Compute a set of random steps in a zero clipped browinan motion.

Parameters

s0	Initial value of an asset
mu	Mean gain for the assest over 1 unit of time
sigma	Standard deviation of gain for the assest over 1 unit of time
step_values	A rank 1 array which will hold the values of the asset over time

Definition at line 358 of file mrffl_stats.f90.

References rand_norm(), and mrffl_config::zero_epsilon.

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