A New Generalized Family of Distributions for Lifetime Data

Abstract

A new class of continuous distributions called the generalized Burr X-G family is introduced. Some special models of the new family are provided. Some of its mathematical properties including explicit expressions for the quantile and generating functions, ordinary and incomplete moments, order statistics and Rényi entropy are derived. The maximum likelihood is used for estimating the model parameters. The flexibility of the generated family is illustrated by means of two applications to real data sets.

The Topp-Leone Odd Burr X-G Family of Distributions: Properties and Applications

“…Evaluation of the models is also carried out using graphical presentations such as the fitted densities, empirical cdf, Kaplan-Meier and probability plots. TLOBX-W distribution was compared with TLOBX-L distribution (in Equation ( 14)), Gamma Weibull (GW) distribution [21], Weibull Lomax (WL) distribution [22], Type I Half Logistic Weibull (TIHLW) distribution [23], Topp-Leone Generalized Exponential (TLGE) distribution [24], Topp-Leone Exponential (TLE) distribution [25] and Generalized odd Burr X-Weibull (GOBXW) distribution [26]. The pdf of the non-nested models are given in Appendix E.…”

A New Class of the Power Function Distribution: Theory and Inference with an Application to Engineering Data

“…In the most recent times, attention towards the generalization of probability distributions has grown phenomenally high. For more insight, see the trustworthy work of Cordeiro and Brito [7], Zaka and Akhter [8], Al Mutairi et al [9], Tahir et al [10], Shahzad et al [11], Ahsan-ul-Haq et al [12], Okorie et al [13], Abdul-Moniem [14], Hassan et al [15], Zaka et al [16], Arshad et al [17], Arshad et al [18,19], Al-Mutairi [20], Alzaatreh et al [21], Gleaton and Lynch [22], Bourguignon et al [23], Afify et al [24], Tahir et al [25], Aldahlan et al [26], Aslam et al [27], Balogun et al [28], Afify et al [29], Mansour et al [30], Mahdavi and Kundu [31], Nassar et al [32], Ijaz et al [33], Klakattawi and Aljuhani [34], Afify et al [35], Alsubie et al [36], Ahmad et al [37], and Nofal et al [38].…”