A Unit Probabilistic Model for Proportion and Asymmetric Data: Properties and Estimation Techniques with Application to Model Data from SC16 and P3 Algorithms

Abstract

In this study, a new one-parameter Log-XLindley distribution is proposed to analyze the proportion data. Some of its statistical and reliability properties, including moments with associated measures, hazard rate function, reversed hazard rate, stress strength reliability, and mean residual life function, are investigated in closed forms which help the researchers for modeling data in a small CPU time. It is found that the density function of the introduced distribution can be used as a statistical tool to model asymmetric data. Moreover, the failure rate function can be utilized to model different types of failures, including increasing, bathtub, and J-shaped. The model parameter is estimated using various estimation approaches to get the best estimator to help us in modeling the real data in a good way with high accuracy. A Monte-Carlo simulation study for different sample sizes is performed to assess the performance of the estimations based on some statistical criteria. Finally, two distinctive data sets from SC16 and P3 algorithms, “estimating unit capacity factors,” are analyzed to illustrate the flexibility of the new model.

Generalized Unit Half-Logistic Geometric Distribution: Properties and Regression with Applications to Insurance

“…Researchers, such as those in [1,2,32], studied the data by dividing it by 100 to rescale it on the unit interval. The GUHLG distribution is fitted to the data, and its performance is compared to that of the UHLG distribution, beta distribution, Kumaraswamy distribution, unit power Weibull (UPW) distribution (see [33]), log-XLindley (LXL) distribution (see [34]), log-Bilal (LB) distribution (see [35]), unit Burr XII (UBXII) distribution (see [36]), unit Burr III (UBIII) distribution (see [37]), unit Weibull (UW) distribution (see [5]) and exponentiated Topp-Leone (ETL) distribution (see [38]). The comparison benchmarks are the −2 , Akaike information criterion (AIC), AIC difference (∆AIC), Akaike weights (ω), Bayesian information criterion (BIC) and Kolmogorov-Smirnov (KS) statistic.…”

Unit Xgamma Distribution: Its Properties, Estimation and Application

“…The random variable X follows UXG if and only if the function η defined in Theorem [24] is of the form (19) Hashmi et al…”

“…There is always a need for other models for modeling bounded data sets. Some such important well-known distributions include Kumaraswamy distribution [2], Unit Burr-III [4], Unit Gompertz distribution [5], Unit Lindley distribution [6], Unit Gamma distribution [7], Unit Birnbaum-Saunders distribution [8], Unit-inverse Gaussian distribution [3], Unit Weibull distribution [9], Unit Logistic distribution [10], Unit modified Burr III distribution [11], unit Rayleigh distribution [12], Unit power-logarithmic distribution [13], odd Frechet power function distribution [14], Unit Burr XIII distribution [15], modified Kumaraswamy distribution [16], Unit Teissier distribution [17], inflated unit Birnbaum-Saunders distribution [18] and log-XLindley distribution [19]. We are motivated to propose a distribution because (i) it can be considered as an appropriate distribution to model the skewed data where other competent models available in the literature may not be adequately fitted; (ii) it can also be applied to model various real data sets in the fields of survival and industrial reliability.…”

An exponentiated XLindley distribution with properties, inference and applications

“…Some authors further introduced some extended forms of XLindley distribution such as Unit-XLindley distribution [ 20 ], Poisson XLindley distribution [ 21 ], Power XLindley distribution [ 22 ], Quasi-XLindley distribution [ 23 ], and new discrete XLindley distribution [ 24 ].…”