# Hamzeh TorabiYazd University · Department of Statistics

Hamzeh Torabi

Professor of Statistics

## About

83

Publications

15,321

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655

Citations

Citations since 2016

Introduction

Additional affiliations

January 2006 - December 2014

January 2005 - present

January 1996 - November 2014

## Publications

Publications (83)

In this paper, we review some existing methods for testing goodness-of-fit based on progressively type-II censored samples in the location-scale family of distributions. Also, some similar procedures and new modifications are proposed. Using Monte Carlo simulation, the powers of the reviewed and proposed tests are compared for the normal and Gumbel...

In this study, a multivariate gamma distribution is first introduced. Then, by defining a new statistic, three control charts called the MG charts, are proposed for this distribution. The first control chart is based on the exact distribution of this statistic, the second control chart is based on the Satterthwaite approximation, and the last is ba...

The aim of this paper is detecting the ordering properties of the smallest claim amounts arising from two sets of independent heterogeneous portfolios in insurance. First, we prove a general theorem that it presents some sufficient conditions in the sense of the hazard rate ordering to compare the smallest claim amounts from two batches of independ...

In this article, we consider a weighted-
$k$
-out-of-
$n$
system having
$m \geq 2$
type of components each with its own positive integer-valued weight, in which the random lifetimes of components are dependent. This system is supposed to work with performance level
$k$
if and only if the total weight of functioning components of all types is...

In this paper, we provide some general results for the usual stochastic ordering of the extreme order statistics arising from two sets of random variables with different marginal distributions and different underlying Archimedean copulas structure. Application to some general models as marginal distributions which are including the well-known semip...

In this paper, by reshaping the hyperbolic secant distribution using Hermite polynomial, we devise a polynomially-modified hyperbolic secant distribution which is more flexible than secant distribution to capture the skewness, heavy-tailedness and kurtosis of data. As a portfolio possibly consists of multiple assets, the distribution of the sum of...

Site period maps at various strain levels were developed for the combined cities of Ottawa and Gatineau in eastern Ontario and western Quebec. These maps were developed to support earthquake response studies in areas containing post-glacial, soft, silty-clayey sediments, which comprise 60% of the urban areas. Approximately 21,700 boreholes and over...

The classical finite mixture model is an effective tool to describe the lifetimes of the items existing in a random sample which are selected from some heterogeneous populations. This paper carries out stochastic comparisons between two classical finite mixture models in the sense of the usual stochastic order, when the subpopulations follow a wide...

Let Xλ1,…,Xλn be independent and non-negative random variables belong to the transmuted-G model and let Yi=IpiXλi,i=1,…,n, where Ip1,…,Ipn are independent Bernoulli random variables independent of Xλis, with E[Ipi]=pi,i=1,…,n. In actuarial sciences, Yi corresponds to the claim amount in a portfolio of risks. In this article, we compare the smallest...

Abstract. Let Xl1 , . . . ,Xln be continuous and dependent non-negative random variables and Yi = IpiXli , i = 1, . . . ,n, where Ip1 , . . . , Ipn are independent Bernoulli random variables independent of Xli ’s, with E[Ipi ] = pi , i = 1, . . . ,n. In actuarial sciences, Yi corresponds to the
claim amount in a portfolio of risks. In this paper, w...

The transmuted-G model is a useful technique to construct some new distributions by adding a parameter. This paper considers stochastic comparisons in the transmuted-G family with different parameters and different baseline distributions in the sense of the usual stochastic, shifted stochastic, proportional stochastic and shifted proportional stoch...

In this paper, we consider inference of the stress-strength parameter, $R$, based on two independent Type-II censored samples from exponentiated Fr\'echet populations with different index parameters. The maximum likelihood and uniformly minimum variance unbiased estimators, exact and asymptotic confidence intervals and hypotheses testing for $R$ ar...

Let $X_{\lambda_1}, \ldots , X_{\lambda_n}$ be independent non-negative random variables belong to the transmuted-G model and let $Y_i=I_{p_i} X_{\lambda_i}$, $i=1,\ldots,n$, where $I_{p_1}, \ldots, I_{p_n}$ are independent Bernoulli random variables independent of $X_{\lambda_i}$'s, with ${\rm E}[I_{p_i}]=p_i$, $i=1,\ldots,n$. In actuarial science...

Let $ X_{\lambda_1},\ldots,X_{\lambda_n}$ be a set of dependent and non-negative random variables share a survival copula and let $Y_i= I_{p_i}X_{\lambda_i}$, $i=1,\ldots,n$, where $I_{p_1},\ldots,I_{p_n}$ be independent Bernoulli random variables independent of $X_{\lambda_i}$'s, with ${\rm E}[I_{p_i}]=p_i$, $i=1,\ldots,n$. In actuarial sciences,...

Let $ X_{\lambda_1},\ldots,X_{\lambda_n}$ be dependent non-negative random variables and $Y_i=I_{p_i} X_{\lambda_i}$, $i=1,\ldots,n$, where $I_{p_1},\ldots,I_{p_n}$ are independent Bernoulli random variables independent of $X_{\lambda_i}$'s, with ${\rm E}[I_{p_i}]=p_i$, $i=1,\ldots,n$. In actuarial sciences, $Y_i$ corresponds to the claim amount in...

In this paper, a three parameters generalization of the power Lindley distribution is introduced. This includes as special cases the power Lindley and Lindley distribution.The new distribution exhibits decreasing, increasing and bathtub hazard rate depending on its parameters. Several statistical properties of the distribution are explored. Then, a...

Due to the flexibility of the failure rate function of the Lomax-exponential distribution, it provides a good alternative for some existing life distributions in modelling positive real data sets in practice. Recently, heterogeneity of components in a system is an appealing topic in some researches. In this paper, we discuss some stochastic compari...

This paper derives some properties of the Marshall–Olkin generalized exponential distribution and shows that this distribution is more flexible than the exponentiated exponential distribution. Then we discuss estimation of the distribution parameters by the methods of moments, maximum likelihood and some new methods based on minimum spacing distanc...

In this paper, two new statistics based on comparison of the theoretical and empirical distribution functions are proposed to test exponentiality. Critical values are determined by means of Monte Carlo simulations for various sample sizes and different significance levels. Through an extensive simulation study, 50 selected exponentiality tests are...

The effect of heterogeneity on order statistics has attracted much attention in recent decades. In this paper, first, we discuss stochastic comparisons of extreme order statistics from independent heterogeneous exponentiated scale samples. These comparisons are made with respect to usual stochastic, reversed hazard rate and likelihood ratio orderin...

In this paper, a new goodness-of-fit test for a location-scale family based on progressively Type-II censored order statistics is proposed. Using Monte Carlo simulation studies, the present researchers have observed that the proposed test for normality is consistent and quite powerful in comparison with existing goodness-of-fit tests based on progr...

In this paper, we propose several statistics for testing uniformity under progressive Type-I interval censoring. We obtain the critical points of these statistics and study the power of the proposed tests against a representative set of alternatives via simulation. Finally, we generalize our methods for continuous and completely specified distribut...

In this paper, we discuss stochastic comparisons of parallel systems with independent heterogeneous exponentiated Nadarajah-Haghighi (ENH) components in terms of the usual stochastic order, dispersive order, convex transform order and the likelihood ratio order. In the presence of the Archimedean copula, we study stochastic comparison of series dep...

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 com...

One of the most important problems in the Bayesian statistical analysis is choosing a suitable prior distribution. In this paper, we introduce a method for hypotheses testing about prior distribution and then give a sequential probability ratio goodness-of-fit test for it. Finally, we give some examples to illustrate the new method.

In this paper, a goodness-of-fit test for normality based on the comparison of the theoretical and
empirical distributions is proposed. Critical values are obtained via Monte Carlo for several sample
sizes and different significance levels.We study and compare the power of forty selected normality
tests for a wide collection of alternative distribu...

We prepare a new method to generate family of distributions. Then, a family of univariate distributions generated by the Gamma random variable is defined. The generalized gamma-Weibull (GGW) distribution is studied as a special case of this family. Certain mathematical properties of moments are provided. To estimate the model parameters, the maximu...

In this paper, the largest order statistics arising from independent heterogeneous gamma random variables with respect to the likelihood ratio order are compared. Let X 1 , .

Some concepts for hypotheses testing about prior density functions based on a primary sample are given. We derive a Neyman-Pearson lemma to find a most powerful goodnessof-fit test for a prior distribution. A main benefit of the proposed test is that Bayesian statisticians may use the proposed test for choosing a suitable prior distribution and use...

In this paper, we estimate the parameters of the Marshall-Olkin generalized exponential distribution under progressive Type-I interval cen-soring based on maximum likelihood, moment method and probability plot. A simulation study is conducted to compare these estimates in terms of mean squared errors and biases. Finally, these estimate methods are...

In this paper, a four parameters extension of the generalized
Lindley distribution is introduced. The new distribution includes the power
Lindley, Lindley, generalized (Stacy) gamma, gamma, Weibull, Rayleigh,
exponential and half-normal distribution. Several statistical properties of
the distribution are explored. Then, a bivariate version of the p...

In this article, we give a new family of univariate distributions generated by the Logistic random variable. A special case of this family is the Logistic-Uniform distribution. We show that the Logistic-Uniform distribution provides great flexibility in modeling for symmetric, negatively and positively skewed, bathtub-shaped, “J”-shaped, and revers...

This paper proposes a simple goodness-of-fit test based on the sample covariance. It is shown that this test is preferable for alternatives of increasing and unimodal failure rate. Critical values for various sample sizes are determined by means of Monte Carlo simulations.
We compare the test based on the sample covariance with tests based on Hoef...

In this paper, some various families constructed from the logit of the generalized Beta, Beta, Kumar, generalized Gamma, Gamma, Weibull, log gamma and Logistic distributions are reviewed. Then a general family of distributions generated from the logit of the normal distribution is proposed. A special case of this family, Normal-Uniform distribution...

A fractional Poisson process has been developed on fractional generalization of the Kolmogorov-Feller equation. In This article, we review the transition from standard Poisson process to its fractional generalization (fractional Poisson process (fPp)). This generalization add a parameter $\alpha\in(0,1]$, and is called the fractional exponent of th...

In this paper, we consider the problem of cooperative spectrum sensing in the presence of the noise power uncertainty. We propose a new spectrum sensing method based on the fuzzy hypothesis test (FHT) that utilizes membership functions as hypotheses for the modeling and analyzing such uncertainty. In particular, we apply the Neyman–Pearson lemma on...

Efficient and reliable spectrum sensing is an essential requirement in cognitive radio networks. One challenge faced in the spectrum sensing is the existence of the noise power uncertainty. This paper proposes a cooperative spectrum sensing scheme using fuzzy set theory to mitigate the noise power uncertainty. In this scheme, the noise power uncert...

n this paper, some various families constructed from the logit of the generalized Beta, Beta,
Kumar, generalized Gamma, Gamma, Weibull, log gamma and Logistic distributions are
reviewed. Then a general family of distributions generated from the logit of the normal
distribution is proposed. A special case of this family, Normal-Uniform distributi...

In this paper, some various families constructed from the logit of the generalized Beta, Beta,
Kumar, generalized Gamma, Gamma, Weibull, log gamma and Logistic distributions are
reviewed. Then a general family of distributions generated from the logit of the normal
distribution is proposed. A special case of this family, Normal-Uniform distribut...

In testing statistical hypotheses, as in other statistical problems, we may be confronted with fuzzy concepts. We first redefine some concepts in testing of fuzzy hypotheses and then introduce a generalized version of the Neyman-Pearson lemma for testing fuzzy hypotheses using r-levels. Finally, two numerical examples are presented to demonstrate t...

This paper considers the simple step-stress model from the Marshall-Olkin generalized exponential distribution when there is time constraint on the duration of the experiment. The maximum likelihood equations for estimating the parameters assuming a cumulative exposure model with lifetimes as the distributed Marshall-Olkin generalized exponential a...

We consider an admissible estimator for the rth power of a scale parameter that is lower or upper bounded in a subclass of the scale-parameter exponential family under the entropy loss function. An admissible estimator for a bounded parameter in the family of transformed chi-square distributions is also given.

Up to present for modelling and analyzing of random phenomenons, some statistical distributions
are proposed. This paper considers a new general class of distributions, generated from
the logit of the gamma random variable. A special case of this family is the Gamma-Uniform
distribution. We derive expressions for the four moments, variance, skewnes...

This paper considers an Extended Generalized Half Logistic distribution. We derive some properties of this distribution and then we discuss estimation of the distribution parameters by the methods of moments, maximum likelihood and the new method of minimum spacing distance estimator based on complete data. Also, maximum likelihood equations for es...

In hypotheses testing, such as other statistical problems, we may confront imprecise concepts. One case is a situation in which hypotheses are imprecise. In this paper, we redefine some concepts about fuzzy hypotheses testing, and then we introduce the sequential probability ratio test for fuzzy hypotheses testing. Finally, we give some examples.

In this article, we first state some relations about the number of partitions of a set under some particular conditions and then we give a new relation about the number of partitions of an n-set, i.e., Bell number B(n). Finally, we give some formulas to count partitions of a natural number n, i.e., partition function P (n).

In hypotheses testing, such as other statistical problems, we may confront imprecise concepts. One case is a situation in which both hypotheses and observations are imprecise. In this paper, we redefine some concepts about fuzzy hypotheses testing, and then we give the Neyman-Pearson lemma for fuzzy hy- potheses testing with fuzzy observations. Fin...

To test “randomness” in spatial point patterns, we propose a test statistic, based on the number of empty-quadrants and then we give some formula about it. Finally, we apply this statistic for testing complete spatial randomness for some two-dimensional examples.

In hypotheses testing, such as other statistical problems, we may confront imprecise concepts. One case is a situation in
which hypotheses are imprecise.
In this paper, we recall and redefine some concepts about fuzzy hypotheses testing, and then we introduce the likelihood ratio
test for fuzzy hypotheses testing. Finally, we give some applied exa...

Fuzzy set theory has been well developed and applied in a wide variety of real problems. Linear models are used frequently in the researches of relations among several variables in a system. In many cases, data are nonprecise (fuzzy). In this article, we proposed a method for least-absolutes estimating of fuzzy parameters in a linear model with fuz...

In some probabilistic problems, there does not exist complete information about the probability of each simple event. In this article, using rough sets theory, we obtain a lower and upper probability for an arbitrary events and then we introduce a measurement for inclusivity of events.

A method for hypotheses testing which makes use of the spacings is proposed. Finally, we give an example.

In hypotheses testing, such as other statistical problems, we may confront imprecise concepts. One case is a situation in which both hypotheses and observations are imprecise. This paper tries to develop a new approach for testing fuzzy hypothesis when the available data are fuzzy, too. First, some definitions are provided, such as: fuzzy sample sp...

Fuzzy set theory has been well developed and applied in a wide variety of real problems. In some probabilistic problems, there does not exist complete information about the probability model. In this paper, using fuzzy rough set theory, we obtain a lower and upper probability for an arbitrary fuzzy random event and then we introduce a measure for i...

p align="LEFT">In some point estimation problems, we may confront imprecise (fuzzy) concepts. One important case is a situation where all observations are fuzzy rather than crisp. In this paper, using fuzzy set theory, we define a fuzzy-valued random variable, a fuzzy unbiased estimator, a fuzzy exponential family, and then we state and prove a Cra...

p>In hypotheses testing, such as other statistical problems, we may confront imprecise concepts. One case is a situation in which both hypotheses and observations are imprecise.
In this paper, we redefine some concepts about fuzzy hypotheses testing, and then we give the sequential probability ratio test for fuzzy hypotheses testing with fuzzy obs...

## Projects

Project (1)