f_distribution Derived Type

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

Computes the cumulative distribution function.

The CDF for a F distribution is given as $$F(x) = I_{d_1 x/(d_1 x + d_2)} \left( \frac{d_1}{2}, \frac{d_2}{2} \right)$$ .

Arguments

Return Value real(kind=real64)

The value of the function.

private pure function fd_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 fd_mean(this) result(rst)

Computes the mean of the distribution.

Arguments

Return Value real(kind=real64)

The mean.

private pure function fd_median(this) result(rst)

Computes the median of the distribution.

Arguments

Return Value real(kind=real64)

The median.

private pure function fd_mode(this) result(rst)

Computes the mode of the distribution.

Arguments

Return Value real(kind=real64)

The mode.

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

Computes the probability density function.

The PDF for a F distribution is given as $$f(x) = \sqrt{ \frac{ (d_1 x)^{d_1} d_{2}^{d_2} }{ (d_1 x + d_2)^{d_1 + d_2} } } \frac{1}{x \beta \left( \frac{d_1}{2}, \frac{d_2}{2} \right) }$$ .

Arguments

Return Value real(kind=real64)

The value of the function.

private subroutine fd_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 fd_variance(this) result(rst)

Computes the variance of the distribution.

Arguments

Return Value real(kind=real64)

The variance.