Upper Record Values from Extended Exponential Distribution

Some recurrence relations are established for the single and product moments of upper record values for the extended exponential distribution by Nadarajah and Haghighi (2011) as an alternative to the gamma, Weibull, and the exponentiated exponential distributions. Recurrence relations for negative moments and quotient moments of upper record values are also obtained. Using relations of single moments and product moments, means, variances, and covariances of upper record values from samples of sizes up to 10 are tabulated for various values of the shape parameter and scale parameter. A characterization of this distribution based on conditional moments of record values is presented

A NOTE ON BAYESIAN ANALYSIS OF DECAPITATED GENERALIZED POISSON DISTRIBUTION UNDER VARIOUS LOSS FUNCTIONS

It is recognized that, for Bayes estimators, the performance depends on the form of the prior distribution and the assumed loss function. This paper resolves the problem of estimation of one parameter decapitated generalized Poisson distribution; using class of improper prior distributions under symmetric and asymmetric loss functions. The statistical performances of the Bayes estimates with respect to different priors and loss functions are compared using mean square error based on simulation study

Identifying Predictors of Childhood Anaemia in North-East India

The objective of this study is to examine the factors that influence the occurrence of childhood anaemia in North-East India by exploring dataset of the Reproductive and Child Health-II Survey (RCH-II). The study population consisted of 10,137 children in the age-group of 0-6 year(s) from North-East India to explore the predictors of childhood anaemia by means of different background characteristics, such as place of residence, religion, household standard of living, literacy of mother, total children ever born to a mother, age of mother at marriage. Prevalence of anaemia among children was taken as a polytomous variable. The predicted probabilities of anaemia were established via multinomial logistic regression model. These probabilities provided the degree of assessment of the contribution of predictors in the prevalence of childhood anaemia. The mean haemoglobin concentration in children aged 0-6 year(s) was found to be 11.85 g/dL, with a standard deviation of 5.61 g/dL. The multiple logistic regression analysis showed that rural children were at greater risk of severe (OR=2.035; p=0.003) and moderate (OR=1.23; p=0.003) anaemia. All types of anaemia (severe, moderate, and mild) were more prevalent among Hindu children (OR=2.971; p=0.000), (OR=1.195; p=0.010), and (OR=1.201; p=0.011) than among children of other religions whereas moderate (OR=1.406; p=0.001) and mild (OR=1.857; p=0.000) anaemia were more prevalent among Muslim children. The fecundity of the mother was found to have significant effect on anaemia. Women with multiple children were prone to greater risk of anaemia. The multiple logistic regression analysis also confirmed that children of literate mothers were comparatively at lesser risk of severe anaemia. Mother\u2019s age at marriage had a significant effect on anaemia of their children as well

On Progressively Type-II Censored Two-Parameter Rayleigh Distribution

Abstract Recently, Rayleigh distribution has received considerable attention in the statistical literature. In this paper, we consider the point and interval estimation of the functions of the unknown parameters of a two-parameter Rayleigh distribution. First, we obtain the maximum likelihood estimators (MLEs) of the unknown parameters. The MLEs cannot be obtained in explicit forms, and we propose to use the maximization of the profile log-likelihood function to compute the MLEs. We further consider the Bayesian inference of the unknown parameters. The Bayes estimates and the associated credible intervals cannot be obtained in closed forms. We use the importance sampling technique to approximate (compute) the Bayes estimates and the associated credible intervals. For comparison purposes we have also used the exact method to compute the Bayes estimates and the corresponding credible intervals. Monte Carlo simulations are performed to compare the performances of the proposed method, and one data set has been analyzed for illustrative purposes. We further consider the Bayes prediction problem based on the observed samples, and provide the appropriate predictive intervals. A data example has been provided for illustrative purposes

Power Modified Lindley Distribution: Properties, Classical and Bayesian Estimation and Regression Model with Applications

In this article, we explore a new probability density function, called the power modified Lindley distribution. Its main feature is to operate a simple trade-off among the generalized exponential, Weibull and gamma distributions, offering an alternative to these three well-established distributions. The proposed model turns out to be quite flexible: its probability density function can be right skewed and its associated hazard rate function may be increasing, decreasing, unimodal and constant. First the model parameters of the proposed distribution are obtained by the maximum likelihood method. Next, Bayes estimators of the unknown parameters are obtained under different loss functions. In addition, bootstrap confidence intervals are provided to compare with Bayes credible intervals. Besides, log power modified Lindley regression model for censored data is proposed. Two real data sets are analyzed to illustrate the flexibility and importance of the proposed model

A Generalization of Generalized Gamma Distributions

<p>For the first time, a new generalization of generalized gamma distribution called the modified generalized gamma distribution has been introduced to provide greater flexibility in modeling data from a practical viewpoint. The new distribution generalizes some recently introduced generalizations of the gamma distribution. Various properties of the proposed distribution, including explicit expressions for the moments, quantiles, mode, moment generating function, mean deviation, mean residual lifetime and expression of the entropies are derived. The distribution is capable of monotonically increasing, decreasing, bathtub-shaped, and upside-down bathtub-shaped hazard rates. The maximum likelihood estimators of unknown parameters cannot be obtained in explicit forms, and they have to be obtained by solving non-linear equations only. Two real data sets have been analyzed to show how the proposed models work in practice.</p