Extended sinepower probability density function

Abstract

The author developed a new probability density function to fit random data, bounded on both extremes and having a single mode within its range of values. This function called sinepower probability density function (SP-PDF) has now been extended to include cases of minimum value having a non-zero probability. Means, standard deviations, skewness coefficients, kurtosis coefficients and criterion indices have been computed and tabulated for use in application to practical problems. To facilitate the numerical work, three more tables and a graph have been appended. A procedure has been described to fit up a SP-PDF for random variables of the double-bounded and single-peaked variety, given their usual statistical parameters, z , s(z), g₁(z) and g₂(z). A numerical example has also been given by means of illustrating the application of the various tables, in fitting up a SP-PDF.