If the standard (mean = 0, scale = 1) normal distribution probability density function is
-[space][space][equation normal01_pdf]
+[equation normal01_pdf]
and the cumulative distribution function
-[space][space][equation normal01_cdf]
+[equation normal01_cdf]
then the [@http://en.wikipedia.org/wiki/Probability_density_function PDF]
of the [@http://en.wikipedia.org/wiki/Skew_normal_distribution skew normal distribution]
with shape parameter [alpha], defined by O'Hagan and Leonhard (1976) is
-[space][space][equation skew_normal_pdf0]
+[equation skew_normal_pdf0]
Given [@http://en.wikipedia.org/wiki/Location_parameter location] [xi],
[@http://en.wikipedia.org/wiki/Scale_parameter scale] [omega],
[@http://en.wikipedia.org/wiki/Skew_normal_distribution transformed],
to the form:
-[space][space][equation skew_normal_pdf]
+[equation skew_normal_pdf]
and [@http://en.wikipedia.org/wiki/Cumulative_distribution_function CDF]:
-[space][space][equation skew_normal_cdf]
+[equation skew_normal_cdf]
where ['T(h,a)] is Owen's T function, and ['[Phi](x)] is the normal distribution.