Alpha-Skew-Logistic Distribution

Abstract

Alpha-skew-Logistic distribution is introduced following the same methodology as those of Alpha-skew-normal distribution (Elal-Olivero, 2010) and Alpha-skew-Laplace distributions (Harandi and Alamatsaz, 2013). Cumulative distribution function (cdf), moment generating function (mgf), moments, skewness and kurtosis of the new distribution is studied. Some related distributions are also investigated. Parameter estimation by method of moment and maximum likelihood are discussed. Closeness of the proposed distribution with alpha-skew-normal distribution is studied. The suitability of the proposed distribution is tested by conducting data fitting experiment and comparing the values of log likelihood, AIC, BIC. Likelihood ratio test is used for discriminating between Alpha-skew-Logistic and logistic distributions.