On presente une approche bayesienne a la modelisation des observations aberrantes et on l'examine en relation avec les membres de la famille exponentielle en general et avec la distribution exponentielle en particulier

Bayes methods for outliers in exponential samples

In the present paper we suggest a procedure for the determination of the number of outliers in exponential and Pareto samples, using the predictive interval approach.

On determining the number of outliers in exponential and Pareto samples

In this paper, we suggest a least squares procedure for the determination of the number of upper outliers in an exponential sample by minimizing sample mean squared error. Moreover, the method can reduce the masking or “swamping” effects. In addition, we have also found that the least squares procedure is easy and simple to compute than test procedure Tk, suggested by Zhang (1998) for determining the number of upper outliers, since Zhang (1998) need to use the complicated null distribution of Tk. Moreover, we give three practical examples and a simulated example to illustrate the procedures. Further, simulation studies are given to show the advantages of the proposed method. Finally, the proposed least squares procedure can also determine the number of upper outliers in other continuous univariate distributions (for example, Pareto, Gumbel, Weibull, etc.).

A note on determining the number of outliers in an exponential sample by least squares procedure

The estimation of power of the scale parameter (σ) is derived for samples from the gamma distribution in the presence of k outliers by using a generalized loss function. Here, estimators of the type hTrare considered for σr, where T is a real valued random variable whose distribution depends on an unknown real parameter σ. We have obtained the Bayes estimate of (∞,σ) under various priors for the same loss function in the presence of k outliers.

On the estimation of the power of the scale parameter of the gamma distribution in the presence of outliers

In the present paper we discuss the estimation of the parameter and survival function of an exponential population It is assumed that the sample based on which the estimation is done, contains k outliers that are also exponentially distributed with parameter, a constant multiple of that of the original distribution

Estimation of Exponential Parameters in the Presence of Outliers

Me consider a situation where the random Tariables are such that (n-1) of them are independent and identically distributed with a probability density function (p.d.f.) , and with probability , the remaining one is distributed with p.d.f. . We will study the behaviour of the Bayesian estimators of the nuisance parameter, mean life and the reliability function under different prior distributions of a and a, The corresponding solutions when the p.d.f. of X's are , will also be outlined.

S.K. Sinha

Papers

Life testing and reliability estimation for non-homogeneous data - a bayesian approach