log_normal_distribution Derived Type

private pure elemental function lnd_cdf(this, x) result(rst)

Computes the cumulative distribution function.

The CDF for a log-normal distribution is given as $$F(x) = \frac{1}{2} \left(1 + erf\left( \frac{\ln{x} - \mu} {\sigma \sqrt{2}} \right) \right)$$

Arguments

Return Value real(kind=real64)

The value of the function.

private pure function lnd_range(this) result(rst)

Gets the defined range for the distribution.

Arguments

Return Value real(kind=real64), dimension(2)

The defined range of the probability distributions [0, infinity). As using a value of infinity may cause issue, this routine returns huge(0.0d0) instead.

private pure function lnd_mean(this) result(rst)

Computes the mean of the distribution

Arguments

Return Value real(kind=real64)

The mean

private pure function lnd_median(this) result(rst)

Computes the median of the distribution

Arguments

Return Value real(kind=real64)

The median

private pure function lnd_mode(this) result(rst)

Computes the mode of the distribution

Arguments

Return Value real(kind=real64)

The mode

private pure elemental function lnd_pdf(this, x) result(rst)

Computes the probability density function.

The PDF for a log-normal distribution is given as $$f(x) = \frac{1}{x \sigma \sqrt{2 \pi}} \exp{\left(- \frac{\left( \ln{x} - \mu \right)^2}{2 \sigma^2} \right)}$$

Arguments

Return Value real(kind=real64)

The value of the function.

private subroutine lnd_recenter(this, x)

Recenters the distribution about the supplied value.

Arguments

private pure elemental function dist_std_var(this, x) result(rst)

Computes the standardized variable for the distribution.

Arguments

Return Value real(kind=real64)

The result.

private pure function lnd_variance(this) result(rst)

Computes the variance of the distribution

Arguments

Return Value real(kind=real64)

The variance