Department of Statistics
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Welcome to the Department of statistics, one of the leading academic and research centers in the field of statistics. With distinguished faculty members, advanced educational facilities, and a dynamic research environment, our faculty provides an excellent platform for the development of knowledge and specialized skills.
Our goal at the Department of statistics is to nurture competent, creative, and dedicated graduates who can play a significant role in scientific, industrial, and social fields. Our academic programs emphasize the latest scientific resources, applied research, and continuous interaction with the industry, preparing students for both professional careers and further academic pursuits.
Ranked set sampling (RSS) is a cost efficient design that has been widely used in agriculture, forestry, ecological and environmental sciences. Frey (Environmental and Ecological Statistics 19(3):309–326, 2012) proposed a sampling scheme based on to allow for partially ordered sets. This scheme permits a ranker to declare ties and then record the tie structure for potential use in statistical analysis. We first introduce two nonparametric maximum likelihood estimators (MLEs) of the population cumulative distribution function (CDF) that incorporate the information for partially ordered sets. We compare the proposed MLEs with the standard nonparametric MLE of the CDF (without utilizing tie information) via Monte Carlo simulation. Motivated by good performance of the new CDF estimators, we further derive two mean estimators for partially ordered sets. Our numerical results from both simulation and real data show that the proposed estimators outperform their competitors provided that the quality of ranking is not low. © Springer Nature Singapore Pte Ltd 2020.
Journal of Statistical Planning and Inference (03783758)36(2-3)pp. 367-383
This paper presents a new series of main effect plans for 2m factorial experiments which permit search and estimation of one nonnegligible effect from two and three factor interactions. Plans in the series are Balanced Arrays (BA) of strength two. A robustness property of such plans is proved. Main effect plans which are near BA of strength two and with the search property, are obtained from the robustness property. Some other plans are also given. © 1993.
Statistical Papers (09325026)39(4)pp. 347-360
Let X be a random variable and X(w) be a weighted random variable corresponding to X. In this paper, we intend to characterize the Pearson system of distributions by a relationship between reliability measures of X and X(w), for some weight function w>0.
Journal of Multivariate Analysis (0047259X)67(2)pp. 190-202
Recently attempts have been made to characterize probability distributions via truncated expectations in both univariate and multivariate cases. In this paper we will use a well known theorem of Lau and Rao (1982) to obtain some characterization results, based on the truncated expectations of a functionh, for the bivariate Gumbel distribution, a bivariate Lomax distribution, and a bivariate power distribution. The results of the paper subsume some earlier results appearing in the literature. © 1998 Academic Press.
Journal of Statistical Planning and Inference (03783758)81(2)pp. 201-207
Many characterization results of the bivariate exponential distribution and the bivariate geometric distribution have been proved in the literature. Recently Nair and Nair (1988b, Ann. Inst. Statist. Math. 40 (2), 267-271) obtained a characterization result of the Gumbel bivariate exponential distribution and a bivariate geometric distribution based on truncated moments. In this note, we extend the results of to obtain a general result, characterizing these two bivariate distributions based on the truncated expectation of a function h, satisfying some mild conditions.
Metrika (1435926X)49(2)pp. 121-126
In this paper, we characterize some multivariate distributions based on a relationship between the multivariate hazard rate, as defined by Johnson and Kotz (1975) and Marshall (1975), and the multivariate mean residual life as defined by Arnold and Zahedi (1988). The results are extensions of the results obtained earlier by Roy (1989, 1990) and Ma (1996, 1997).
Statistics and Probability Letters (01677152)49(3)pp. 263-269
A direct approach to measure uncertainty in the residual life time distribution has been initiated by Ebrahimi (1996, Sankhya Ser. A 58, 48-57) and explored further by Ebrahimi and Pellerey (1995) and Ebrahimi and Kirmani (1996). In this paper, some new properties of the proposed measure in connection to order statistics and record values are derived. The generalized Pareto distribution has been widely used in the literature. We have also given several characterizations of this distribution in terms of the proposed measure.
Handbook of Statistics (01697161)20pp. 199-214
Asadi, M.,
Ebrahimi, N.,
Hamedani, G.,
Soofi, E.S. Journal of Applied Probability (00219002)41(2)pp. 379-390
A formal approach to produce a model for the data-generating distribution based on partial knowledge is the well-known maximum entropy method. In this approach, partial knowledge about the data-generating distribution is formulated in terms of some information constraints and the model is obtained by maximizing the Shannon entropy under these constraints. Frequently, in reliability analysis the problem of interest is the lifetime beyond an age t. In such cases, the distribution of interest for computing uncertainty and information is the residual distribution. The information functions involving a residual life distribution depend on t, and hence are dynamic. The maximum dynamic entropy (MDE) model is the distribution with the density that maximizes the dynamic entropy for all t. We provide a result that relates the orderings of dynamic entropy and the hazard function for distributions with monotone densities. Applications include dynamic entropy ordering within some parametric families of distributions, orderings of distributions of lifetimes of systems and their components connected in series and parallel, record values, and formulation of constraints for the MDE model in terms of the evolution paths of the hazard function and mean residual lifetime function. In particular, we identify classes of distributions in which some well-known distributions, including the mixture of two exponential distributions and the mixture of two Pareto distributions, are the MDE models.
Communications in Statistics - Theory and Methods (1532415X)34(2)pp. 475-484
One of the most important types of system structures is the parallel structure. In the present article, we propose a definition for the mean residual life function of a parallel system and obtain some of its properties. The proposed definition measures the mean residual life function of a parallel system consisting of n identical and independent components wider the condition that n -i, i = 0, 2,..., n -1, components of the system are working and other components of the system have already failed. It is shown that, for the case where the components of the system have increasing hazard rate, the mean residual life function of the system is a nonincreasing function of time. Finally, we will obtain an upper bound for the proposed mean residual life function. Copyright © Taylor & Francis, Inc.
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