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Keywords
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Logistic distribution, Mixture distribution, Skew Logistic distribution, maximum likelihood estimator,
Likelihood ratio test
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Abstract
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In this paper, the generalized mixture of standard logistic and skew logistic is introduced as a new class
of distribution. Some important mathematical properties of this novel distribution are discussed along with a graphical
presentation of the density function. These properties include moment generating function, mth order moment, mean
deviation, characteristic function, entropy, among others. Moreover, a location scale type extension of the proposed
distribution is considered, and the maximum likelihood estimation method for this model is presented. To examine the
performance of the estimated parameters of the proposed distribution, a simulation study is also conducted using the rejection sampling method. Furthermore, an application using two real-life data sets are also illustrated. Finally, the likelihood ratio
test is performed to study the discrepancies between proposed model with their counterparts.
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