• Communications for Statistical Applications and Methods
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• v.28 no.2
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• pp.99-118
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• 2021

In this paper, we introduce an extended form of the inverse power Lomax model via Marshall-Olkin approach. We call it the Marshall-Olkin inverse power Lomax (MOIPL) distribution. The four- parameter MOIPL distribution is very flexible which contains some former and new models. Vital properties of the MOIPL distribution are affirmed. Maximum likelihood estimators and approximate confidence intervals are considered under Type I censored samples. Maximum likelihood estimates are evaluated according to simulation study. Bayesian estimators as well as Bayesian credible intervals under symmetric loss function are obtained via Markov chain Monte Carlo (MCMC) approach. Finally, the flexibility of the new model is analyzed by means of two real data sets. It is found that the MOIPL model provides closer fits than some other models based on the selected criteria.

• Journal of applied mathematics & informatics
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• v.41 no.6
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• pp.1275-1301
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• 2023

This paper introduced the Weibull Marshall-Olkin Power Lomax (WMOPL) distribution. The statistical aspects of the proposed model are presented, such as the quantiles function, moments, mean residual life and mean deviations, variance, skewness, kurtosis, and reliability measures like the residual life function, and stress-strength reliability. The parameters of the new model are estimated using six different methods, and simulation research is illustrated to compare the six estimation methods. In the end, two real data sets show that the Weibull Marshall-Olkin Power Lomax distribution is flexible and suitable for modeling data.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.501-505
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• 2012

In this paper, general classes of continuous distributions are characterized by considering the conditional expectations of functions of upper record statistics. The specific distribution considered as a particular case of the general class of distribution are Exponential, Exponential Power(EP), Inverse Weibull, Beta Gumbel, Modified Weibull(MW), Weibull, Pareto, Power, Singh-Maddala, Gumbel, Rayleigh, Gompertz, Extream value 1, Beta of the first kind, Beta of the second kind and Lomax.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.475-477
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• 2014

Lee and Lim (2009) state three characterizations of Loamax, exponential and power function distributions, the proofs of which, are based on the solutions of certain second order non-linear differential equations. For these characterizations, they make the following statement : "Therefore there exists a unique solution of the differential equation that satisfies the given initial conditions". Although the general solution of their first differential equation is easily obtainable, they do not obtain the general solutions of the other two differential equations to ensure their claim via initial conditions. In this very short report, we present the general solutions of these equations and show that the particular solutions satisfying the initial conditions are uniquely determined to be Lomax, exponential and power function distributions respectively.