PsiMetalogSPT(min, max, quantiles, prob, prop_fcns)

This distribution is constructed by a symmetric percentile triplet. The cumulative probabilities are {prob, 0.5, 1-prob}, where 0 < prob < 0.5. The corresponding quantile set is a 3-element array/range of quantiles. The optional min and max arguments have the same meaning of lower and upper bounds as in the PsiMegalog. This distribution can be truncated, shifted, correlated, compounded etc. through the use of property functions.

There are 3 optional cases for this distribution:

  • Both min and max are missing which results in an unbounded distribution

PsiMetalogSPT(, , {35, 50, 75}, 0.1)

  • Only min exists which results in a semi-bounded distribution

PsiMetalogSPT(0, , {35, 50, 75}, 0.1) semi-bounded

  • Both min and max exist which results in a bounded distribution

PsiMetalogSPT(0, 100, {35, 50, 75}, 0.1)

Note:  Analytic moments are available only for unbound distributions. Kurtosis is always computed.