Some Properties and Applications of Burr III-Weibull Distribution

A New Class of Generalized Burr III Distribution for Lifetime Data

For the first time, the Generalized Gamma Burr III (GGBIII) is introduced as an important model for problems in several areas such as actuarial sciences, meteorology, economics, finance, environmental studies, reliability, and censored data in survival analysis. A review of some existing gamma families have been presented. It was found that the distributions cannot exhibit complicated shapes such as unimodal and modified unimodal shapes which are very common in medical field. The Generalized Gamma Burr III (GGBIII) distribution which includes the family of Zografos and Balakrishnan as special …

混合删失下广义威布尔分位数的控制图

Control Chart for Generalized Weibull Quantiles under Hybrid Censoring

本文针对混合删失下广义威布尔分布分位数，提出基于自助法和休哈特型控制图的监控方案，利用EM算法推导最大似然估计并通过仿真和医疗实例验证其检测失控信号的有效性。

On The Robustness of Epsilon Skew Extension for Burr III Distribution on Real Line

The Burr III distribution is used in a wide variety of fields of lifetime data analysis, reliability theory, and financial literature, etc. It is defined on the positive axis and has two shape parameters, say $c$ and $k$. These shape parameters make the distribution quite flexible. They also control the tail behavior of the distribution. In this study, we extent the Burr III distribution to the real axis and also add a skewness parameter, say $\varepsilon$, with epsilon-skew extension approach. When the parameters $c$ and $k$ have a relation such that $ck \approx 1 $ or $ck < 1 $, it is skewed…

Extreme values for Benedicks-Carleson quadratic maps

We consider the quadratic family of maps given by $f_{a}(x)=1-a x^2$ with $x\in [-1,1]$, where $a$ is a Benedicks-Carleson parameter. For each of these chaotic dynamical systems we study the extreme value distribution of the stationary stochastic processes $X_0,X_1,...$, given by $X_{n}=f_a^n$, for every integer $n\geq0$, where each random variable $X_n$ is distributed according to the unique absolutely continuous, invariant probability of $f_a$. Using techniques developed by Benedicks and Carleson, we show that the limiting distribution of $M_n=\max\{X_0,...,X_{n-1}\}$ is the same as that whi…