Statistics

The present paper deals with the problem of estimating the finite population variance using two-phase sampling scheme in the presence of random non-response. In this paper, we have suggested some families of factor-type estimators of population variance utilizing the information on an auxiliary variable with unknown population variance. The properties of the suggested families of estimators have been discussed in detail. The optimum estimators of the suggested families have also been pioneered out. The theoretical results have been demonstrated through some real data sets. A simulation study has also been carried out to support the theoretical results.

In this paper, various generalized imputation procedures have been suggested and their corresponding families of estimators of population mean have been considered. Asymptotic expressions for biases and mean squared errors have been obtained. Optimum conditions are investigated at which the proposed family of estimators has minimum mean squared errors. It has been shown that the proposed imputation procedures and the resulting families of estimators due to Singh and Horn (2000), Ahmed et al. (2006), Shukla and Thakur (2008) and Pandey et al (2015) are members of the suggested procedures and estimators. The results of this paper are general and of immense useful.

The effect of Second Order Autoregressive (AR-2) model and non-normality on the power function of the control chart for known ? is studied. The power function is derived by considering the first four terms of an Edgeworth series for AR-2 model. The values of power function for three situation viz. when the roots are (i) real and distinct (ii) real and equal and (iii) complex conjugate along with case when there is no dependency are presented.

According to WHO maternal and child health services can be defined as promoting, preventing, therapeutic or rehabilitation facility or care for the mother and child. In India and developing world, many women suffer from complications during pregnancy and delivery care. Utilization of maternal and child care services during pregnancy and delivery care will helps in reducing the mortality and morbidity of mother and her child. An effort has been made in this study to assess the maternal and child health care services utilization among the women. Third round of National Family Health Survey (NFHS-III) has been used in this study. The study selected 32,222 women age 15-49 who had at least one birth in five year prior to the survey. Empowered Action Group states and Assam has been selected to carry-out this study. In this study we illustrate the Andersen’s Behavioural Model of Health Care Utilization. The model describes factors that inhibit or facilitate access to health care, and how these factors are applied in the process of seeking and using health services. The result showed that only 19% of the women delivery takes place in health facilities while 31.7% received assistance during delivery from skilled provider in EAG states and Assam. Utilization of maternal health services was significantly low among rural women as compared to their urban counterparts. Result also showed that the educational status of the mother, household wealth quintile is found to be strong indicators of utilization of maternal health care services. 

In the present manuscript, a new class of estimators of population mean has been proposed. This estimator makes use of the information on the population median of the study variable. The expressions for the bias and the mean squared error of the proposed class of estimators have been derived up to the first order of approximation. The optimum value of the characterizing scalar which minimizes the mean squared error of the proposed class has been obtained. The minimum mean squared error for this optimum value of the characterizing scalar is also obtained. The proposed estimator has been compared with the competing estimators of population mean which make use of auxiliary information. A numerical study is also carried out to judge the performances of the proposed and the competing estimators.

Social and physical status of a woman is always considered as very important factor for affecting the fertility. And it becomes more important when we talk about developing countries like India. Our study consists of fertility influenced by women status in EAG states of India.In consideration of that study we use the weighted data of EAG states reported in NFHS-III (2005-06). In that perspective we have approximately 54000 sampling units in which approx. 45000 females are considered as not pregnant and not in amenorrhea. For this we take women population in between age group 15-49 years. A multivariate model was fitted for living children for different socio-demographic variables taken as influencing factors. For background characters we consider 8 different variables on basis of socio- demographic status norms. There is significant association in between contraception use to the living children in light of background characters controlling. Within the range of 95 percent confidence interval the odds ratio for education and living children for those who ever used any contraception is 1.77 (1.71-1.82)and 6.65 (6.39-6.95) respectively. By which we can define a significant association between ever using contraception to education and living children based on women’s socio-demographic status. This implies that if the strength of status of women make uplift then fertility condition will be better in population

A dynamic graphical display and regression diagnostics is proposed for examining the validating assumption of the error term in a multiple regression modeling. Residual plots were used to detect the regression assumption of homocesdasticity tendency. Independence of the error term was diagnosed through Durbin Watson Test statistic or scatter plots of residuals against time order. Letter value displays were used to detect approximate normality through mid-summaries values. The error term validation were characterized with the residuals following an even distribution of scatter plots along a horizontal line through zero point, high (r2), minimal standard error of estimates for the predictors, the Cp statistic close to P+1 which means a small biased, the P value less than 0.05(level of significant), and lack of bivariate high correlations among the predictors

A method of constructing equireplicate Variance Balanced (VB) and Efficiency Balanced (EB) design with unequal block sizes is proposed using 2n-symmetrical factorial design by deleting the control treatment and merging all the main effects with highest order interaction separately. Further optimality of the constructed design has been checked and found it to be universally optimal.

This paper suggests a new exponential ratio-type estimator for estimating the population variance using information of two auxiliary attributes in SRSWOR based on the adaption of the estimator presented by Lu et al. (2014). Problem is extended to the case of two phase sampling. The expressions for the mean square error of the proposed estimator have been derived. The proposed estimator has been compared theoretically with the usual unbiased estimator, usual ratio type estimator, estimator proposed by Chauhan et al. (2009) and the estimator proposed by Singh et al. (2009) and the conditions under which the proposed estimator are better than some existing estimators have also been given. An empirical study has also been carried out using two population data sets to demonstrate the efficiencies of the proposed estimator.

In this article, we proposed an SEIVR mathematical model of the transmission dynamics of infectious diseases among infants taking into consideration passive immunization, treatment of the exposed infants at latent period and the infectious diseases treatment. The basic reproductive number of the mathematical model was obtained using the next generation matrix method. It is generally known that if the number is less than one, the infectious disease will die out with time and if it is greater than one, the disease will spread and become endemic in the community. The epidemiological interpretation of this threshold parameter (basic reproductive number) is connected to the local and global stability of a disease – free equilibrium.