On a modified Burr XII distribution having flexible hazard rate shapes

Abstract

In this paper, we propose a new three-parameter modified Burr XII distribution based on the standard Burr XII distribution and the composition technique developed by [14]. Among others, we show that this technique has the ability to significantly increase the flexibility of the former Burr XII distribution, with respect to the density and hazard rate shapes. Also, complementary theoretical aspects are studied as shapes, asymptotes, quantiles, useful expansion, moments, skewness, kurtosis, incomplete moments, moments generating function, stochastic ordering, reliability parameter and order statistics. Then, a Monte Carlo simulation study is carried out to assess the performance of the maximum likelihood estimates of the modified Burr XII model parameters. Finally, three applications to real-life data sets are presented, with models comparisons. The results are favorable for the new modified Burr XII model.

Quantifying Risk Using Loss Distributions

“…All the PDFs of the loss distributions in the Burr family have a monotonically decreasing, right-skewed tails; see [15]. The Burr distribution is well recognized in probability theory with many applications in agriculture, biology, etc., see [20].…”

Estimation of Entropy for Generalized Rayleigh Distribution under Progressively Type-II Censored Samples

“…They studied the statistical characteristics and some properties of the generalized Rayleigh distribution, and pointed out that it can be used as a lifetime distribution and to characterize intensity data. Surles et al [3] and Al-khedhari et al [4] discussed parameter estimation for this distribution using different techniques.…”

“…Burr Type X and Burr Type XII distributions are important distributions in survival analysis problems. They were two of the twelve types of lifetime distributions proposed by Burr in 1942, and since their proposal, their applications and statistical inference theory have received widespread attention and research [3,4]. In recent years, with the deepening of research, the generalized Rayleigh distribution has been widely applied in fields such as wireless communication, radar signal processing, image processing, seismology, astronomy, and ecology [5][6][7].…”