t_distribution Derived Type

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

Computes the cumulative distribution function.

The CDF for Student's T-Distribution is given as $$F(t) = \int_{-\infty}^{t} f(u) \,du = 1 - \frac{1}{2} I_{x(t)} \left( \frac{\nu}{2}, \frac{1}{2} \right)$$ where $$x(t) = \frac{\nu}{\nu + t^2}$$ .

Arguments

Return Value real(kind=real64)

The value of the function.

private pure function td_mean(this) result(rst)

Computes the mean of the distribution.

Arguments

Return Value real(kind=real64)

The mean.

private pure function td_median(this) result(rst)

Computes the median of the distribution.

Arguments

Return Value real(kind=real64)

private pure function td_mode(this) result(rst)

Computes the mode of the distribution.

Arguments

Return Value real(kind=real64)

The mode.

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

Computes the probability density function.

The PDF for Student's T-Distribution is given as $$f(t) = \frac{ \Gamma \left( \frac{\nu + 1}{2} \right) } { \sqrt{\nu \pi} \Gamma \left( \frac{\nu}{2} \right) } \left( 1 + \frac{t^2}{\nu} \right)^{-(\nu + 1) / 2}$$ .

Arguments

Return Value real(kind=real64)

The value of the function.

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 td_variance(this) result(rst)

Computes the variance of the distribution.

Arguments

Return Value real(kind=real64)

The variance.