Research & reviews journal of statistics (vol3, issue1) by STM Journals Publication

Research & Reviews Journal of Statistics (RRJHS)

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Volume 1, Issue 1-3 Compilation 2012

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ISSN : 2348-7909

Jan - April 2014

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I take the privilege to present the hard copy compilation for the [Volume 3 Issue (1)] of Research & Reviews: Journal of Statistics. The intension of RRJoST is to create an atmosphere that stimulates creativeness, research and growth in the area of Journal of Statistics. The development and growth of the mankind is the consequence of brilliant Research done by eminent Scientists and Engineers in every field. RRJoST provides an outlet for Research findings and reviews in areas of Statistics found to be relevant for National and International recent developments & research initiative. The aim and scope of the Journal is to provide an academic medium and an important reference for the advancement and dissemination of Research results that support high level learning, teaching and research in the domain of Statistics. Finally, I express my sincere gratitude and thanks to our Editorial/ Reviewer board and Authors for their continued support and invaluable contributions and suggestions in the form of authoring writeups/ reviewing and providing constructive comments for the advancement of the journals. With regards to their due continuous support and co-operation, we have been able to publish quality Research/Reviews findings for our customers base. I hope you will enjoy reading this issue and we welcome your feedback on any aspect of the Journal.

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Research & Reviews : Journal of Statistics

Contents

1. Estimation of Mean with Imputation of Missing Data in Stratified Random Sampling Narendra Singh Thakur, Kalpana Yadav, Sharad Pathak

2. Hybrid Poisson Distribution Sampath Sundaram, Deepa S P

3. Individual Patient Data Meta-Analysis using Proportional Hazard Models Md. Nuruzzaman Forhad, Md. Erfanul Hoque, Md. Belal Hossain

4. A New Form of Sam-Solai's Multivariate Generalized Normal Distribution G.S. David Sam Jayakumar, A. Solairaju, A. Sulthan

Research & Reviews: Journal of Statistics ISSN: 2348-7909 Volume 3, Issue 1 www.stmjournals.com

Estimation of Mean with Imputation of Missing Data in Stratified Random Sampling Narendra Singh Thakur1*, Kalpana Yadav2, Sharad Pathak3 1

Department of Mathematics and Statistics, Banasthali University, Banasthali, Rajasthan, India 2 Department of Statistics, Delhi University, Delhi, India 3 Department of Mathematics and Statistics, Dr. H. S. Gour Central Univesity, Sagar (M.P), India

Abstract In this paper we present some imputation methods to estimate the population mean in presence of missing data under stratified sampling design. The suggested methods are discussed in simple random sampling as well. The expression of bias and MSE are derived in the form of population parameters using the concept of large sample approximation upto first order. A Comparative study is considered between stratified and simple random sampling. The empirical study is carried out over two real populations.

Keywords: Estimation, missing data, bias, mean squared error (M.S.E.), stratified random sampling, SRSWOR, large sample approximation

Research & Reviews: Journal of Statistics ISSN: 2348-7909 Volume 3, Issue 1 www.stmjournals.com

Hybrid Poisson Distribution Sampath Sundaram1*, Deepa S P2 1

Department of Statistics, University of Madras, Chennai 600005, India Department of Statistics, SDNB Vaishnav College for Women, Chromepet, Chennai, India

Abstract In this paper, hybrid version of Poisson distribution using the Chance Theory due to Liu (2008) is developed. The process of computing chance values of various events, mean and variance of hybrid poisson distribution using an evolutionary algorithm, namely, genetic algorithm are discussed with some illustrative examples.

Keywords: Hybrid variable, chance distribution, hybrid binomial distribution, hybrid poisson distribution

Research & Reviews: Journal of Statistics ISSN: 2348-7909 Volume 3, Issue 1 www.stmjournals.com

Individual Patient Data Meta-Analysis using Proportional Hazard Models Md. Nuruzzaman Forhad1*, Md. Erfanul Hoque2*, Md. Belal Hossain1 1

Department of Statistics, Biostatistics & Informatics, University of Dhaka, Dhaka, Bangladesh 2 Department of Statistics, Jagannath University, Dhaka, Bangladesh

Abstract One alternative to classical meta-analytic approaches is known as individual patient data (IPD) meta-analysis. Rather than depending on summary statistics calculated for individual studies, IPD meta-analysis analyzes the complete data from all included studies. The IPD meta-analysis is considered the gold-standard for synthesizing survival data. In this paper, an attempt has been made to introduce the use of parametric and semi-parametric proportional hazard models to perform one and two-step IPD metaanalysis of time-to-event outcomes. Three parametric PH models: exponential PH model, Weibull PH model, log-logistic PH model and one semi-parametric PH model: Cox PH model have been used for this purpose. The parameter estimation procedure has been illustrated in two-step approach and finally hazard ratio has been calculated. For the illustration of the proposed framework, the demographic health survey (DHS) data for ten countries has been used. An investigation is made to assess the impact of place of residence on child mortality by applying our proposed IPD meta-analysis methods and finally make a comparison of the rate of child mortality between rural and urban area. Here different studies (different countries) show contradictory results but after performing proposed meta-analysis approach the actual impact of place of resident on child mortality has been found. The given approach provides an appropriate guideline to get the better estimated values by using the appropriate model to the data. If the distribution of the data is known then one can easily gets the appropriate result using this approach.

Keywords: Hazard ratio, individual patient data, proportional hazard model, meta-analysis

Research & Reviews: Journal of Statistics ISSN: 2348-7909 Volume 3, Issue 1 www.stmjournals.com

A New Form of Sam-Solai’s Multivariate Generalized Normal Distribution G.S. David Sam Jayakumar1*, A. Solairaju2, A. Sulthan3 Jamal Mohamed College, Tiruchirappalli–620 020, South India, India

Abstract This paper proposed a new generalization of family of Sarmanov type Continuous multivariate symmetric probability distribution with reference to a new form of SamSolai’s Multivariate Generalized normal distribution from univariate case. Further, we find its Marginal, Conditional distributions, Generating functions and also discussed it’s special cases.The shape parameter played a significance role and it determines the family of some existing multivariate distributions as subclass of the proposed multivariate generalized normal distribution. The special cases include the transformation of MVGND into Generalized log-normal distribution and Sam-Solai’s Multivariate log-Laplace distribution. The following results are redundant: (1) SamSolai’s Multivariate Laplace distribution, (2) Sam-Solai’s Multivariate Gaussian normal distribution, (3) Sam-Solai’s Multivariate mixture of normal-Laplace distribution, (4) Sam-Solai’s Multivariate and (5) Sam-Solai’s Multivariate log-normal distribution. Moreover, it is found that the conditional variance of Sam-Solai’s Multivariate generalized conditional normal distribution is heteroskedastic and the correlation co-efficient between any two generalized normal random variables determined by the shape parameters .Finally, area values of the Bivariate Generalized normal distribution are extracted and bivariate probability surfaces are visualized for different values of shape parameters.

Keywords: Sarmanov type, Sam-Solai’s, multivariate generalized normal distribution, conditional variance, heteroskedastic, shape parameter