International Journal of Mathematics and Statistics™
The main aim of the International Journal of Mathematics and Statistics™ [ISSN 0974-7117 (Print), ISSN 0973-8347 (Online)] is to publish refereed, well-written original research articles, and studies that describe the latest research and developments in the area of mathematics and statistics. This is a broad-based journal covering all branches of mathematics, statistics and interdisciplinary research. International Journal of Mathematics & Statistics is a peer-reviewed online journal and is published Three times a year. International Journal of Mathematics and Statistics (IJMS) is reviewed, abstracted and indexed in the past by the Mathematical Reviews; MathSciNet; Zentralblatt für Mathematik (Zentralblatt MATH); Statistical Theory and Method Abstracts (STMA-Z), Current Index to Statistics (CIS) [ The Current Index to Statistics (CIS) is a joint venture of the American Statistical Association & Institute of Mathematical Statistics, USA], International Abstracts in Operations Research (IAOR), Indian Science Abstracts; Academic keys; JournalSeek, Ulrich's Periodicals Directory, International Statistical Institute (ISI, Netherlands) Journal Index, IndexCopernicus, Getcited…
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Generalized Modified Exponential-G Family of Distributions: Its Properties and Applications
A new family of continuous distributions called generalized modified exponential-G family is proposed. The probability density and cumulative distribution function are expressed as infinite linear mixtures of exponentiated-G distribution. Important statistical properties such as moment generating function, distribution of order statistics, power moments, asymptotes and shapes of the proposed family are investigated. The maximum likelihood estimation of the parameters is presented. To check the suitability the proposed model is compared with its submodels and also with a few useful lifetime models by conducting three data fitting experiments with real-life data sets.
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A Class of Generalized Estimators for Population Mean Using Two Auxiliary Variables under Non-Response
Non-response is a very common problem among large scale sample surveys. In this paper an imputation-based study has been conducted under non-response using two auxiliary variables for the estimation of population mean of study variable. Proposed estimator is generalized exponential-cum-factor type estimator, it’s bias and MSE’s have been derived and special cases have also been discussed. Empirical study has also been done to show its efficiency over other existing estimators.
Some Improved Estimators Using Auxiliary Variables in Post-Stratification
Through this paper we have tried to manifest the problem of estimation of Population Mean using auxiliary variables in post-stratified sampling. We have suggested improved estimators and have derived the expressions for the Mean Square errors. In order to verify the efficiencies of the suggested estimators we have carried out an empirical study for which we have considered two natural datasets.
Mortality modelling at advanced ages using a nonparametric approach
The mortality amongst people of advanced ages in developed countries has been decliningfor several decades and will continue to do so in the foreseeable future. While the falling mortality rate is not uniform, it is important to model and understand this event since the ageing of a population will inevitably lead to major economic and social transformation. In this paper, we consider the problem of modelling demographic data at advanced ages by adopting an efficient nonparametric approach, the fixed–design local polynomial regression. A new nonparametric mortality model is proposed with specific application to the Australian mortality rate for the 60 plus age group. The proposed model outperforms existing parametric models used in modelling mortality rate and has the advantage that its implementation avoids the often cumbersome parameter estimation step that is required in the parametric approach. It has also been observed that existing parametric models are country specific whereas the proposed nonparametric model easily adapts itself to any given population. We apply the mean residual life function to estimate the gender specific life expectancy curves. Finally, noting the importance of studying the modal age at death in modern populations, we estimate the gender specific modal age at death.
Transient Behavior of a Markovian N-Policy Queue with Balking Re-Service and Closedown Time
The objective of this paper is to investigate the non-stationary behavior of an M/M/1 queue with N- policy, re-service, balking and closedown time. The server stays dormant (off state) until N customers accumulate in the queue and then starts an exhaustive service (on state). When the system reaches the empty state, the server resumes closedown work. After the closedown, the server stays idle and waits N accumulate for service. When the Nth customer enters the queue, the server starts an exhaustive service. After finishing the service, the unsatisfied customers may request another service (re-service) immediately. The arrivals may either balk or join the queue when the system size is less than N. The system distributions are derived for the model under consideration.The important system performance indices are obtained and numerical simulations are also presented.
An Efficient Exponential Ratio-type Estimator in Post-Stratification Using Variable Transformation
Following Tailor and Tailor [11], we propose an exponential ratio-type estimator in post-stratified sampling using variable transformation. The proposed estimator, under certain conditions are shown to be more efficient than some existing estimators, including the usual post-stratified estimator, separate ratio-type estimator for estimating the population mean of the variable under study variable in case of post-stratification, usual dual to separate ratio-type estimator in case of post-stratification, Chouhan [2] and Lone and Tailor [4]. The efficiency of the proposed estimator has also shown through numerical illustrations.
Two phase sampling exponential type estimators for population mean using auxiliary attribute in the presence of non-response
In this paper, two phase sampling exponential ratio and product type estimators for population mean using auxiliary attribute in the presence of non-response have been proposed. The expressions for mean square error of the proposed estimators in condition of fixed sample sizes are obtained. The comparisons of the proposed estimator with the relevant estimator are also given. In situation of fixed cost, the minimum mean square errors of the proposed estimators are obtained and in case of specified variance, the expected total cost is also obtained. The performance of the proposed estimators over the relevant estimator is checked by an empirical study.
Generalized Class of Dual to Product cum Dual to Ratio estimator for Population Mean with Imputation of Missing Data in Two-Phase Sampling Scheme
This paper aims to deal with the problem of non-response in the study variable, by proposing a generalized class of estimator for estimating population mean under the framework of two-phase sampling design by using auxiliary information and also the expressions for bias and mean square error are derived. Further, theoretical results stating supremacy of the proposed estimators, over the existing estimators by empirical illustration based on different data sets are shown.