Classical and Bayesian analysis with fitting radiation data: Using a new truncated distribution

This paper presents a new flexible distribution, called the truncated inverse power Ishita distribution. The aim is to transpose the remarkable flexibility of the two-parameter inverse power Ishita distribution to the interval [0,1]. The essential statistical characteristics of the proposed model are calculated, encompassing its moments, incomplete moments, Bonferroni and Lorenz curves, mean, variance, skewness, kurtosis, moment-generating function, quantile function, and order statistics. Employing eight conventional estimation techniques: maximum likelihood, least squares, weighted least squares, Cramér-Von-Mises, maximum product of spacings, Anderson-Darling, right-tail Anderson-Darling, and the percentile method. A simulation study was performed to demonstrate the practical applicability of the proposed distribution. The Bayesian method for estimating unknown parameters uses the Markov chain Monte Carlo approach. The goodness of fit of the proposed model was evaluated using two accurate radiation data sets compared to competing models.