arXiv subjects

Ali Dolati

Publications and source records attributed to Ali Dolati.

4 recordsLinked to original sources

arXiv2018

Stochastic comparisons between the extreme claim amounts from two heterogeneous portfolios in the case of transmuted-G model

Let $X_{λ_1}, \ldots , X_{λ_n}$ be independent non-negative random variables belong to the transmuted-G model and let $Y_i=I_{p_i} X_{λ_i}$, $i=1,\ldots,n$, where $I_{p_1}, \ldots, I_{p_n}$ are independent Bernoulli random variables independent of $X_{λ_i}$'s, with ${\rm E}[I_{p_i}]=p_i$, $i=1,\ldots,n$. In actuarial sciences, $Y_i$ corresponds to the claim amount in a portfolio of risks. In this paper we compare the smallest and the largest claim amounts of two sets of independent portfolios belonging to the transmuted-G model, in the sense of usual stochastic order, hazard rate order and dispersive order, when the variables in one set have the parameters $λ_1,\ldots,λ_n$ and the variables in the other set have the parameters $λ^{*}_1,\ldots,λ^{*}_n$. For illustration we apply the results to the transmuted-G exponential and the transmuted-G Weibull models.

stat.AP↗

arXiv2018

Ordering the smallest claim amounts from two sets of interdependent heterogeneous portfolios

Let $ X_{λ_1},\ldots,X_{λ_n}$ be a set of dependent and non-negative random variables share a survival copula and let $Y_i= I_{p_i}X_{λ_i}$, $i=1,\ldots,n$, where $I_{p_1},\ldots,I_{p_n}$ be independent Bernoulli random variables independent of $X_{λ_i}$'s, with ${\rm E}[I_{p_i}]=p_i$, $i=1,\ldots,n$. In actuarial sciences, $Y_i$ corresponds to the claim amount in a portfolio of risks. This paper considers comparing the smallest claim amounts from two sets of interdependent portfolios, in the sense of usual and likelihood ratio orders, when the variables in one set have the parameters $λ_1,\ldots,λ_n$ and $p_1,\ldots,p_n$ and the variables in the other set have the parameters $λ^{*}_1,\ldots,λ^{*}_n$ and $p^*_1,\ldots,p^*_n$. Also, we present some bounds for survival function of the smallest claim amount in a portfolio. To illustrate validity of the results, we serve some applicable models.

q-fin.RM↗

arXiv2018

Stochastic comparisons of the largest claim amounts from two sets of interdependent heterogeneous portfolios

Let $ X_{λ_1},\ldots,X_{λ_n}$ be dependent non-negative random variables and $Y_i=I_{p_i} X_{λ_i}$, $i=1,\ldots,n$, where $I_{p_1},\ldots,I_{p_n}$ are independent Bernoulli random variables independent of $X_{λ_i}$'s, with ${\rm E}[I_{p_i}]=p_i$, $i=1,\ldots,n$. In actuarial sciences, $Y_i$ corresponds to the claim amount in a portfolio of risks. In this paper, we compare the largest claim amounts of two sets of interdependent portfolios, in the sense of usual stochastic order, when the variables in one set have the parameters $λ_1,\ldots,λ_n$ and $p_1,\ldots,p_n$ and the variables in the other set have the parameters $λ^{*}_1,\ldots,λ^{*}_n$ and $p^*_1,\ldots,p^*_n$. For illustration, we apply the results to some important models in actuary.

q-fin.RM↗

arXiv2017

A new notion of majorization with applications to the comparison of extreme order statistics

In this paper, we use a new partial order, called the f-majorization order. The new order includes as special cases the majorization , the reciprocal majorization and the p-larger orders. We provide a comprehensive account of the mathematical properties of the f-majorization order and give applications of this order in the context of stochastic comparison for extreme order statistics of independent samples following the Frechet distribution and scale model. We discuss stochastic comparisons of series systems with independent heterogeneous exponentiated scale components in terms of the usual stochastic order and the hazard rate order. We also derive new result on the usual stochastic order for the largest order statistics of samples having exponentiated scale marginals and Archimedean copula structure.

math.ST↗