Marshall-Olkin Lindley-Log-logistic distribution: Model, properties and applications

Abstract

The authors introduce a new generalized distribution called the Marshall-Olkin Lindley-Log-logistic (MOLLLoG) distribution and discuss its distributional properties. The properties include hazard function, quantile function, moments, conditional moments, mean and median deviations, Bonferroni and Lorenz curves, distribution of the order statistics and Rényi entropy. A Monte Carlo simulation study was used to examine the bias, relative bias and mean square error of the maximum likelihood estimators. The betterness of the new distribution compared to other distributions is illustrated by means of two real life datasets.

Application of Odd Lomax log-logistic distribution to cancer data

“…Using the families mentioned above and others, the generalized log-logistic distributions introduced are Marshall-Olkin extended Fisk distribution [ 12 ], exponentiated Fisk distribution [ 13 ], McDonald Fisk distribution [ 14 ], Kumaraswamy odd fisk distribution [ 15 ], Kumaraswamy Marshall-Olkin Fisk distribution [ 16 ], Marshall-Olkin Lindley Fisk distribution [ 17 ], the beta Fisk distribution [ 3 ] and the inverse Lomax Fisk distribution [ 18 ].…”

The New Exponentiated Half Logistic-Harris-G Family of Distributions with Actuarial Measures and Applications

“…As a result of the extra parameters introduced, the tail weight and entropy of a density function can be controlled, depending on the resulting distribution. Some of the well-known families, to mention just a few of these, are as follow: the Marshall-Olkin-G, by [1], the beta-G, by [2], the transmuted-G, by [3], the gamma-G, by [4], the Kumaraswamy-G, by [5], the exponentiated generalized-G by [6], the T-X family, by [7], the logistic-G, by [8], the Weibull-G, by [9], and the odd log-logistic-G by [10], the type II half logistic family of distributions, by [11], the odd log-logistic Topp-Leone G family of distributions, by [12], the type II half logistic Kumaraswamy distribution, by [13], the exponentiated half-logistic odd Lindley-G family of distributions, by [14], the type II kumaraswamy half logistic family of distributions, by [15], the half logistic log-logistic Weibull distribution, by [16], the half logistic modified Kies exponential distribution, by [17], a class of distributions which includes the normal ones by [18], the stable symmetric family of distributions, by [19], towards the establishment of a family of distributions that best fits any data set, by [20], and the generation of distribution functions, by [21].…”

Marshall-Olkin-Odd Power Generalized Weibull-G Family of Distributions with Applications of COVID-19 Data

“…More recently, general results on the Marshall-Olkin family of distributions were given by Barreto-Souza et al [3]. Moakofi et al [21] developed the Marshall-Olkin Lindley-Log-logistic distribution. Krishna et al [16] established Marshall-Olkin Fréchet distribution and its applications.…”