Inference of Truncated Lomax Inverse Lomax Distribution with Applications

Abstract

This paper introduces a modified form of the inverse Lomax distribution which offers more flexibility for modeling lifetime data. The new three-parameter model is provided as a member of the truncated Lomax-G procedure. The new modified distribution is called the truncated Lomax inverse Lomax distribution. The density of the new model can be represented as a linear combination of the inverse Lomax distribution. Expansions for quantile function, moment generating function, probability weighted moments, ordinary moments, incomplete moments, inverse moments, conditional moments, and Rényi entropy measure are investigated. The new distribution is capable of monotonically increasing, decreasing, reversed J-shaped and upside-down shaped hazard rates. Maximum likelihood estimators of the population parameters are derived. Also, the approximate confidence interval of parameters is constructed. A simulation study framework is established to assess the accuracy of estimates through some measures. Simulation outcomes show that there is a great agreement between theoretical and empirical studies. The applicability of the truncated Lomax inverse Lomax model is illustrated through two real lifetime data sets and its goodness-of-fit is compared with that of the recent models. In fact, it provides a better fit to these data than the other competitive models.

Engineering Applications with Stress-Strength for a New Flexible Extension of Inverse Lomax Model: Bayesian and Non-Bayesian Inference

“…Bayesian estimates of the ILo distribution parameters using several approximation approaches were discussed by Jan and Ahmad [13]. Some extended forms for ILo distribution have been presented (see, for example, [14][15][16][17][18]). The SS (stress-strength) reliability estimator of the ILo model, based on extreme and median ranked set sampling, has been presented, respectively, by Al-Omari et al [19] and Hassan et al [20].…”

Analysis of Household Income, Expenditure and Consumption Survey Research Data for North Sinai Governorate in Egypt Using Length Biased Truncated Lomax Distribution

“…where w(t) is a non-negative weight function and E(w(t)) > 0. Distinct selections of w(t)produce different WDs, that is Numerous new modifications and expansions of the Lo distribution have subsequently been developed, such as; beta Lo [21], gamma-Lo [12], Weibull Lo [27], power Lo [25], generalized Lo [5], beta transmuted Lo [19], alpha power Lo [10], truncated Lo inverse Lo [3], and distributions among others. Some recent studies about Lo distribution can be found in [8,9].…”