Ahmad Parsian

University of Tehran | UT ·  School of Mathematics, Statistics and Computer Sciences

In this paper we introduce a broad family of loss functions based on the concept of Bregman divergence. We deal with both Bayesian estimation and prediction problems and show that all Bayes solutions associated with loss functions belonging to the introduced family of losses satisfy the same equation. We further concentrate on the concept of robust...

This paper deals with the dependent left censoring scheme when the survival time variable and censoring variable are dependent and have Marshal–Olkin bivariate exponential distribution. We use the expectation–conditional maximization algorithm for finding the maximum likelihood estimates of the unknown parameters. From Bayesian point of view, based...

This paper is devoted to robust Bayes sample size determination under the quadratic loss function. The idea behind the proposed approach is that the smaller a chosen posterior functional, the more robust the posterior inference. Such desired posterior functional has been taken, in the literature, as the range of posterior mean over a class of prior...

In this paper we investigate the task of parameter learning of Bayesian networks and, in particular, we deal with the prior uncertainty of learning using a Bayesian framework. Parameter learning is explored in the context of Bayesian inference and we subsequently introduce Bayes, con- strained Bayes and robust Bayes parameter learning methods. Baye...

Discrete lifetime data are very common in engineering and medical researches. In many cases the lifetime is censored at a random or predetermined time and we do not know the complete survival time. There are many situations that the lifetime variable could be dependent on the time of censoring. In this paper we propose the dependent right censoring...

This paper deals with Bayes, robust Bayes, and minimax predictions in a subfamily of scale parameters under an asymmetric precautionary loss function. In Bayesian statistical inference, the goal is to obtain optimal rules under a specified loss function and an explicit prior distribution over the parameter space. However, in practice, we are not ab...

In this paper, under Type-I progressive hybrid censoring sample, we obtain maximum likelihood estimator of unknown parameter when the parent distribution belongs to proportional hazard rate family. We derive the conditional probability density function of the maximum likelihood estimator using moment generating function technique. The exact confide...

Let \Pi_1 and \Pi_2 denote two gamma populations with common known shape parameter \alpha > 0 and unknown scale parameters \theta_1 and \theta_2, respectively. Let X1 and X2 be two independent random variables from \Phi_1 and \Phi_2, and X(1) <= X(2) denote the ordered statistics of X1 and X2. Suppose the population corresponding to the largest X(2...

In this paper, we assume that the lifetimes have a two-parameter Pareto distribution and discuss some results of progressive Type-II censored sample. We obtain maximum likelihood estimators and Bayes estimators of the unknown parameters under squared error loss and a precautionary loss functions in progressively Type-II censored sample. Robust Baye...

Protein-protein interactions (PPIs) are highly important because of their main role in cellular processes and biochemical pathways; therefore, PPI can be very useful in the prediction of protein functions. Experimental techniques of PPI detection have certain drawbacks; hence computational methods can be used to complement wet lab techniques. Such...

Let II1 and II2 denote two gamma populations with common known shape parameter α > 0 and unknown scale parameters θ1 and θ2, respectively. Let X1 and X2 be two independent random variables from II1 and II2, and X(1) ≤ X(2) denote the ordered statistics of X1 and X2. Suppose the population corresponding to the largest X(2) or the smallest X(1) obser...

Robust Bayesian methodology deals with the problem of explaining uncertainty of the inputs (the prior, the model, and the loss function) and provides a breakthrough way to take into account the input's variation. If the uncertainty is in terms of the prior knowledge, robust Bayesian analysis provides a way to consider the prior knowledge in terms o...

This paper deals with Bayes, robust Bayes and minimax predictions in a subfamily of scale parameters under an asymmetric precautionary loss function. In Bayesian statistical inference the goal is to obtain optimal rules under a specified loss function and an explicit prior distribution over the parameter space. However, in practice, we are not able...

In this article, we deal with a dependent middle censoring with a censoring interval of fixed length, where the lifetime and lower bound of censoring interval are variables with a Marshall-Olkin bivariate exponential distribution. In this setup, we derive maximum likelihood estimates of the unknown parameters, using some iterative method. We also p...

In this article, we consider paired survival data, in which pair members are subject to the same right censoring time, but they are dependent on each other. Assuming the Marshall-Olkin Multivariate Weibull distribution for the joint distribution of the lifetimes (X 1, X 2) and the censoring time X 3, we derive the joint density of the actual observ...

Prediction of a future observation on the basis of currently observed data is demanded in many theoretical and applied problems. In this paper, we introduce prediction of a future observation from scale models under the general entropy prediction loss function and deal with Bayes and Posterior Regret Gamma Minimax prediction and obtain general form...

In this paper, we consider the prediction problem of a future observation in a family of scale parameter models under a class of precautionary prediction loss function in the context of Bayes and robust Bayes methodology. Under three members of the precautionary prediction loss functions, which are suitable members when considering scale invariant...

In this article, we consider the right random censoring scheme in a discrete setup when the lifetime and censoring variables are independent and have geometric distributions with means 1/1 and 1/2, respectively. We first obtain the Maximum Likelihood and Method of Moment estimators of the unknown parameters. We also find the Bayes and Posterior R...

Estimation based on the left-truncated and right randomly censored data arising from a general family of distributions is considered. In the special case, when the random variables satisfy a proportional hazard model, the maximum likelihood estimators (MLEs) as well as the uniformly minimum variance unbiased estimators (UMVUEs) of the unknown param...

For estimating an unknown parameter θ, we introduce and motivate the use of balanced loss functions of the form $${L_{\rho, \omega, \delta_0}(\theta, \delta)=\omega \rho(\delta_0, \delta)+ (1-\omega) \rho(\theta, \delta)}$$, as well as the weighted version $${q(\theta) L_{\rho, \omega, \delta_0}(\theta, \delta)}$$, where ρ(θ, δ) is an arbitrary los...

This is a short paper discussing the admissibility and inadmissibility of linear estimators of p-1 based on mth record value from a sequence of geometric distribution.

In this paper we consider the discrete middle censoring where lifetime, lower bound and length of censoring interval are variables with geometric distribution. We obtain the likelihood function of observed data and derive the MLE of the unknown parameter using EM algorithm. Also we obtain the Bayes estimator of the unknown parameter under squared e...

Censored data arise naturally in a number of fields, particularly in problems of reliability and survival analysis. There are several types of censoring; in this article, we shall confine ourselves to the right randomly censoring type. Under the Bayesian framework, we study the estimation of parameters in a general framework based on the random cen...

Let $X_{1}$ and $X_{2}$ be two independent random variables from gamma populations $\Pi_1,\Pi_2$ with means $\alpha\theta_1$ and $\alpha\theta_2$ respectively, where $\alpha(>0)$ is the common known shape parameter and $\theta_1$ and $\theta_2$ are scale parameters. Let $X_{(1)}\leq X_{(2)}$ denote the order statistics of $X_1$ and $X_2$. Suppose t...

We consider dependent right censoring when the lifetime and censoring variables have a A. W. Marshall and I. Olkin [J. . Appl. Probab. 4, 291–302 (1967; Zbl 0155.24001)] bivariate exponential distribution and obtain MLEs, MMEs and UMVUEs of the unknown parameters. The Bayes estimators as well as the Posterior Regret Gamma Minimax (PRGM) estimators...

A semi-parametric class of distributions that includes several well-known lifetime distributions such as exponential, Weibull (one parameter), Pareto, Burr type XII and so on is considered in this paper. Bayes estimation of parameters of interest based on k-record data under balanced type loss functions is developed; and in some cases the admissibi...

Nous étudions ici l'estimation de R=P(X<Y), quand X et Y sont des variables aleatoires qui suivent la loi bivariate Weibull et X est censurée à Y. On obtient la loi marginale pour les données observées et on en tire MLE,UMVUE,MME de R. Ainsi on obtient les estimateurs de Bayes sur la fonction SEL. On a effectué une simulation de Monte-Carlo pour co...

We study the problem of predicting future k-records based on k-record data for a large class of distributions, which includes several well-known distributions such as: Exponential, Weibull (one parameter), Pareto, Burr type XII, among others. With both Bayesian and non-Bayesian approaches being investigated here, we pay more attention to Bayesian p...

Robust Bayesian analysis is connected with the effect of changing a prior within a class Γ instead of being specified exactly. The multiplicity of prior leads to a collection or a range of Bayes actions. It is interesting not only to investigate the range of estimators but also to recommend the optimal procedures. In this article, we deal with post...

For a vast class of discrete model families with cdf's F[theta], and for estimating [theta] under squared error loss under a constraint of the type [theta][set membership, variant][0,m], we present a general and unified development concerning the minimaxity of a boundary supported prior Bayes estimator. While the sufficient conditions obtained are...

Recent studies have shown that the T 2 control chart with variable sampling intervals (VSI) and/or variable sample sizes (VSS) detects process shifts faster than the traditional T 2 chart. This article extends these studies for processes that are monitored with VSI and VSS using double warning lines (T 2 —DWL). It is assumed that the length of time...

For estimating an unknown parameter [theta], we introduce and motivate the use of the balanced-type loss function: , where 0[less-than-or-equals, slant][omega][less-than-or-equals, slant]1, q([theta]) is a positive weight function, and [delta]0 is a general "target" estimator. Developments and various examples are given with regards to the issues o...

The problem of estimating the standard deviation of a normal distribution with known mean μ is considered. The estimator minimizing the mean squared error among all constant multiples of the second sample moment about either μ or X ¯ is found.

For ap-variate normal mean with known variances, the model proposed by Zellner (1986,J. Amer. Statist. Assoc.,81, 446–451) is discussed in a slightly different framework. A generalized Bayes estimate is derived from a three-stage Bayes point of view under the asymmetric loss function, and the admissibility of such estimators is proved.

In Ghosh and Parsian (1981), the Lindley-Smith (1972) linear estimates of the multinonnal mean vector are shown to be generalized Bayes with respect to symmetric bowl shaped loss both when the common variance is known and unknown . The admissibility of such estimators is also proved in both these oases. The present paper gencralizes the findings of...

For the p-variate normal mean with known variances, the Lindley-Smith (1972) estimators are shown to be generalized Bayes under symmetric bowl shaped loss, and the admissibility of such estimators is proved. Also, when the variance-covariance matrix is unknown, generalized Bayes estimators are proposed under symmetric bowl shaped loss, and their ad...

For the p-variate Poisson mean, under the sum of weighted squared error losses, weights being reciprocals of variances, a class of proper Bayes minimax estimates dominating the usual estimate, namely the sample mean is produced. An example is given to illustrate this. The interrelation of our results with those of Clevenson and Zidek is pointed out...

Consider p independent distributions each belonging to the one parameter exponential family with distribution functions absolutely continuous with respect to Lebesgue measure. For estimating the natural parameter vector with p ≥ p0 (p0 is typically 2 or 3), a general class of estimators dominating the minimum variance unbiased estimator (MVUE) or a...