Weibull distributions are widely used in reliability and survival analysis. In this paper, different methods to estimate the shape and scale parameters of the two-parameter Weibull distribution have been reviewed and compared, based on the bias, mean square error and variance. Because a theoretical comparison is not possible, an extensive simulation study has been conducted to compare the perfo...

This paper address the problem of online learning finite statistical mixtures of exponential families. A short review of the Expectation-Maximization (EM) algorithm and its online extensions is done. From these extensions and the description of the k-Maximum Likelihood Estimator (k-MLE), three online extensions are proposed for this latter. To illustrate them, we consider the case of mixtures o...

Loss of (Fisher) information, whose concept was de ned by Fisher, is one of important measures of asymptotic e ciency. Based on Fisher information, this paper studies fourth and fth order asymptotic e ciency of estimators in a curved exponential family of distributions with a structural parameter vector. In particular, we show that the bias-corrected MLE with a certain bias correction factor is...

The problem of estimating linear functions of ordered scale parameters of two Gamma distributions is considered under entropy loss. A necessary and sufficient condition for the maximum likelihood estimator (MLE) to dominate the crude unbiased estimator (UE) is given on two non-negative coefficients. Furthermore, improvement on the UE of the reciprocal of each scale parameter is also obtained un...

Probability distributions perform a very significant role in the field of applied sciences, particularly reliability engineering. Engineering data sets are either negatively or positively skewed and/or symmetrical. Therefore, flexible distribution is required that can handle such sets. In this paper, we propose new family lifetime to model aforementioned This proposed known as “New Modified Exp...

In this article, we present a Markov Bernoulli Lomax (MB-L) model, which is obtained by countable mixture of and distributions, with decreasing unimodal hazard rate function (HRF). The new model contains Marshall- Olkin distributions as special case. mathematical properties, behavior probability density (PDF), HRF, rth moments, moment generating (MGF) minimum (maximum) Markov-Bernoulli Geometri...

This paper concerns the estimation of the parameters that describe a stable distribution. Stable distributions are characterised by four parameters which can be estimated using a number of methods and although approximate maximum likelihood estimation (MLE) techniques do exist, they are computationally intensive. There are a number of techniques that are much faster thanMLE and these are the fo...

We draw here on the relation between the Cauchy and hyperbolic secant distributions to prove that the MLE of the scale parameter of Cauchy distribution is log-normally distributed and to study the properties of a Hodges-Lehmann type estimator for the scale parameter. This scale estimator is slightly biased but performs well even on small samples regardless of the location parameter. The asympto...

This paper provides the Bayes estimators of the failure rate and reliability function for a one-parameter, exponential distribution by utilizing a point guess estimate of the parameter. For deriving the Bayes estimators, the prior distributions are chosen such that they are centered at the known prior values of parameters. The validity of proposed estimators is examined with respect to their ma...

A novel version of the exponential Weibull distribution known as extended (ExEW) is developed and examined using Lehmann alternative II (LAII) generating technique. The new distributions basic mathematical properties are derived. maximum likelihood estimation (MLE) technique used to estimate unknown parameters proposed distribution. estimators’ performance further assessed Monte Carlo simulatio...