Characterizations of the Amoroso distribution based on a simple relationship between two truncated moments are presented. A remark regarding the characterization of certain special cases of the Amoroso distribution based on hazard function is given. We will also point out that a sub-family of the Amoroso family is a member of the generalized Pearson system.
Authors:Gholamhoss G. Hamedani and Gholamhoss G. Hamedani
This is a follow up to our previous works characterizing well-known univariate continuous distributions based on a simple relationship between two truncated moments. Three of the distributions considered here unify many distributions employed for size distribution of income (which were characterized in our previous works). Another three distributions characterized here, were first introduced in the context of minimum dynamic discrimination information approch to probability modeling.
We present here characterizations of the most recently introduced continuous univariate distributions based on: (i) a simple relationship between two truncated moments; (ii) truncated moments of certain functions of the 1th order statistic; (iii) truncated moments of certain functions of the nth order statistic; (iv) truncated moment of certain function of the random variable. We like to mention that the characterization (i) which is expressed in terms of the ratio of truncated moments is stable in the sense of weak convergence. We will also point out that some of these distributions are infinitely divisible via Bondesson’s 1979 classifications.
Authors:G. Hamedani, Hans Volkmer, and J. Behboodian
First, we recall a concept which is called sub-independence. This concept is stronger than that of uncorrelatedness but a lot weaker than independence. The concept of sub-independence, unlike that of uncorrelatedness, does not depend on the existence of any moments. Then, we consider a particular bivariate mixture to construct a pair (X, Y), which is sub-independent but not independent.
Authors:M. Ahsanullah, G. Hamedani, and J. Wesołowski
López-Blázquez and Weso lowski  introduced the top-k-lists sequence of random vectors and elaborated the usefulness of such data. They also developed the distribution of top-k-lists and their properties arising from various probability distributions, such as standard exponential distribution and uniform distribution on (0, 1). In this paper, we study the linearity of regressions inside top-k-lists and then based on this study we present characterizations of certain distributions.
Authors:Morad Alizadeh, Mahdi Rasekhi, Haitham M. Yousof, Thiago G. Ramires, and G. G. Hamedani
In this article, a new four-parameter model is introduced which can be used in mod- eling survival data and fatigue life studies. Its failure rate function can be increasing, decreasing, upside down and bathtub-shaped depending on its parameters. We derive explicit expressions for some of its statistical and mathematical quantities. Some useful characterizations are presented. Maximum likelihood method is used to estimate the model parameters. The censored maximum likelihood estimation is presented in the general case of the multi-censored data. We demonstrate empirically the importance and exibility of the new model in modeling a real data set.
Authors:Morad Alizadeh, Saeid Tahmasebi, Mohammad Reza Kazemi, Hamideh Siyamar Arabi Nejad, and G. Hossein G. Hamedani
In this paper, we introduce a new three-parameter generalized version of the Gompertz model called the odd log-logistic Gompertz (OLLGo) distribution. It includes some well-known lifetime distributions such as Gompertz (Go) and odd log-logistic exponential (OLLE) as special sub-models. This new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a decreasing, increasing and bathtub-shaped failure rate function depending on its parameters. Some mathematical properties of the new distribution, such as closed-form expressions for the density, cumulative distribution, hazard rate function, the kth order moment, moment generating function and the quantile measure are provided. We discuss maximum likelihood estimation of the OLLGo parameters as well as three other estimation methods from one observed sample. The flexibility and usefulness of the new distribution is illustrated by means of application to a real data set.