Abstract: This study considers the use of Bayesian methodology in mortality projection for India by using Logistic and Brass Model. Many ways have been proposed for projecting future mortality however in doing so less emphasis has been paid on the age specific death rates (ASDR). In this work, two versions of parametric models are proposed for projecting mortality rates. Model-1 describe the projecting life expectancy at birth then converted into ASDR while Model-2 is the improve version are useful for probabilistic projection of ASDR under Bayesian Hierarchical Model (BHM). In order to evaluate the adequacy of the model proposed, we fit the observed and estimated data sets of several years. Furthermore, we compare these with other model already existed and use in the current mortality projection method. The ASDR data from Sample Registration System during 1971-2012 for India is used in study.

Abstract: The analysis of family building process has been very popular among demographers and statisticians. The observed length of birth interval of married women are taken as indicators of their reproductive performances and useful for estimating fecundability, parity progression ratio etc. First birth interval (FBI) is such indicator of fertility near marriage. The value of mean FBI depends to a large extent on whether it is obtained for women of a specific age or marital duration or whether the data for all women are pooled. This article generally deals with the analysis of distribution of FBI under different sampling frames. The frames are prepared according to female’s marital duration, number of children born to her.

In study of fertility ,if we consider a cohort of married females and follow the individuals in it month by month to find the duration of first birth, we face the selection effect of heterogeneity i.e., female who are more fecund will conceive sooner and drop outs for observation will be those who are less fecund.

Female having marital duration T can never have the value of first conception X greater than T. Hence, for shorter T, the observed values of X will be small since many female are subject to truncation as they did not give a birth in (0, T). To avoid truncation bias, analysis of first birth interval was done only with the female of higher marital duration. Consequently data of recently married female is not utilised.

Hence, how the distribution of first conception behaves in the shorter marital duration is investigated in Heterogeneous Group of Female. A methodology is proposed to find the estimate of fecundability including recently married women of Heterogeneous Group of Female.

Abstract: In this paper, we have selected DNA of Hepataitis B virus which has affected the people of Eastern India. The DNA sequences have been collected from NCBI with nucleotide sequence as data base. Here, two distributions viz. generalized poisson distribution and generalized negative binomial distribution have been used for our study and comparison has been done regarding which distribution is giving a better prediction and conclusions have been drawn accordingly.

Abstract: Child mortality is a good indicator of level and quality of health care as well as socio-economic condition of country. The modelling of child mortality is an interested area for the researchers of population sciences. During with time a lot of models proposed by researcher and study the various variables which are affect child mortality. But changing with time with identifies the factors that cause changes in child mortality as well as better model for child mortality is essential. Here, the objective of this paper is to attempts study the relevant relationship of demographic and socio-economic variable with child mortality by Bayesian Modelling. Data is taken from District level health and facility survey-3 occurs in 2006-2007 .The female that complete their reproductive life span taken as subject from Uttar Pradesh. In this study we take two different models to predict the child mortality. Model -1 take uniform death probability model under binomial setup and model 2, take the number of child deaths per women follow binomial distribution for the probability of child death(p) for each female affect by socio-economic variable using logit link function. This all the setup perform in Bayesian framework under the MCMC technique.

Abstract: In the present paper we have projected Sex Ratio at Birth in Uttar Pradesh using Linear regression model, assuming lower and upper limit from the past estimates of Fraction of Female at Birth from the Sample Registration System data available from 1995 to 2015 under Bayesian Methodology. Bayesian method involves complicated mathematical terms in posterior distribution. Most of them can be handled by Monte Carlo Markov chain (MCMC) simulation method. The MCMC method is a repetition procedure of generating samples from our distribution. We have used this method for handling the difficulties which arises due to typical mathematical terms that involves expected value of the function of a random variable. Parameters of the model have been estimated using MCMC Technique in Bayesian Procedure. We have assumed Non-informative prior distribution to implement the Bayesian approach for the parameter estimation. We used a Bayesian approach, implemented in WinBUGS, to check the suitability of linear regression model for the growth of Sex Ratio at Birth data obtained from different SRS reports of Uttar Pradesh. Our main focus was to develop the methodology and program for Bayesian Projection.

Abstract: In this project work the weather data of Coimbatore district from the year 1901 to 2002 was analysed using by statistical and joint probability techniques to identify the month in which the correlation coefficient is high between rainfall and maximum temperature, rainfall and minimum temperature and between maximum and minimum temperature. Then the corresponding joint probabilities and marginal probabilities and regression equations are calculated for the month at which the correlation coefficient is high. The dataset consists of (i) monthly rainfall data, (ii) monthly average maximum temperature data, and (iii) monthly average minimum temperature of Coimbatore district from 1901 to 2002. All the computations are implemented using Scilab script. The discrete probability distribution, marginal probability mass function and conditional expectations are also calculated between the months in which the correlation coefficient is high. The aim of this work is to predict the month at which rainfall is maximum and to predict the change in atmospheric temperature as a result of increase in rainfall and other environmental factors and to interpret the results by means of Statistical and Joint Probability analysis.

Abstract: Use of auxiliary information is a well established practice in sampling theory for improving the efficiency of estimators for estimating population parameters in sample surveys. But the collection of auxiliary information also increases the cost of survey. Use of median of study variable may be an important attempt in this aspect. The present paper concerns with the estimation of population mean of the study variable by utilizing the known median of the study variable. A generalized ratio type estimator has been proposed for this purpose. The expressions for the bias and mean squared error of the proposed estimator have been derived up to the first order of approximation. The optimum value of the characterizing scalar has also been obtained. The minimum value of the proposed estimator for this optimum value of the characterizing scalar is also obtained. A theoretical efficiency comparison of the proposed estimator has been made with the mean per unit estimator, usual ratio estimator of Cochran (1940), usual regression estimator of Watson (1937),Bahl and Tuteja (1991), Kadilar (2016) and Subramani (2016) estimators. Through the numerical study, the theoretical findings are validated and it has been found that proposed estimator performs better than the existing estimators.

Abstract: When the rate parameter is not known, it is customary that the ‘plug-in’ control limits are constructed by replacing the parameter by its suitable estimator in the control limits of known parameter case. In general, it is assumed that the efficacy of the control chart with estimated parameter(s) depends on accuracy of the estimator and hence, the choice of estimator becomes crucial. In this paper, we study the ‘plug-in’ control limits of Shewhart-type exponential charts using various estimators, biased too, of the rate parameter and make an attempt to select the one who outperforms than the others. The preliminary studies show that an estimator can be chosen so that the corresponding ‘plug-in’ chart’s performance is optimal in terms of one of desired criteria, for example, average run length. In the following, three optimal design charts are proposed and their performances are then examined. The comparisons are also made with the traditional Phase II exponential chart using Maximum likelihood estimator (MLE). Two illustrative examples are given and some conclusions are offered.

Keywords: Conditional average run length; Exponential distribution; Optimal design chart; Out-of-control performance; Phase II control limits; Times between events.

Abstract: The use of applied biology in treatment of cancer by using mathematical modeling to perceive the tumor growth kinetics has been enhanced over the past couple of decades. The quantitative optimization of this phenomenon explained with mathematical modeling has a massive impact in the field of clinical investigation. In the present study, some mathematical models namely generalized logistic function, Gompertz function, Gompertz tumor growth model, Gompertz differential equation have been discussed to understand the dynamics of tumor growth.All these models exhibit similar kind of behavior, basically follow the sigmoid growth curve i.e.at the early stage the cell density increases steadily.Soon after, proliferating cells approach an exponential growth rate and eventually decline in a negative stimulation phase as the cell population draws near the threshold of the carrying capacity.

Abstract: There is a huge volume of personal data available with the Government and private organizations. The initiatives by Indian Government like Digital India, UID-Aadhaar and smart city have added to the already growing pool of personal data. The initiative is to integrate the government departments and the people of India ensuring government services and data to be made available to the citizens electronically. For collection of data, periodically statistical agencies conduct surveys on industry, consumer expenditure, census, labour and employment, health etc. However, for information processing and decision making, data needs to be shared (Open Government Data platform) and sometimes the form and extent of such disclosure has the potential of divulging the identity of the responding unit along with the information provided. There always exists a tension between Statistical Disclosure Control (SDC) and dissemination for the Government statistical agencies – the tension between individual privacy and data utility. In this paper we evaluate a particular SDC method towards a successful trade-off between confidentiality and usability of data from any large scale sample survey. The methodology is applied to the Consumer Expenditure Survey data of National Sample Survey Office (NSSO), GoI from a few selected states. We find that our proposed method successfully minimizes disclosure risk while maintaining a relatively low level of information loss and remaining relatively very successful in classification.

Abstract: In multivariate stratified sample surveys, a compromise criterion is needed to estimate the unknown population means of different characteristics defined on each unit of the population. In this paper, the importance of stochastic optimization is studied by considering three models of stochastic optimization in sample allocation problems of sample surveys. Also a cost function is defined by including labour cost. A numerical illustration is included for the practical utility of the proposed method.

Abstract: Child mortality is the phenomenon to consider a great consideration in the development scenario to any country. So going for the proper planning of the development we need the proper estimates of that condition to justify ourself. It is evident that defining the direct measurement of that phenomenon is very tedious job. So we made to indirect approach of measurement with use of probability models. In this study we try to establish a model by which we can get the estimates of male and Female child mortality separately and simultaneously with the help of National Family Health Survey- III(2005-06) data of Empowered Action Group(EAG) states of India.

Abstract: Industrial production refers to the output of the industry establishments and covers sectors such as mining, manufacturing and public utilities (electricity, water and gas).This indicator is measured in an index based on a reference period that expresses change in volume of production output. This project deals with the Index of Industrial Production (Base: 1993-94=100) at two digit industry level indices (NIC-1987) with weights from April 1994 to June 2011, annual average (Apr-Mar) indices .The industrial products involved are : food production, cotton, wool fibre, jute, chemical, petroleum, mining, manufacturing, electricity , general.

The motive of this project is to analyse the industrial production data using time series analysis and draw inference. The dataset is collected from Open Government Data Platform India. The primary objective is to study the effects of trend on Index of Industrial Production (IIP) in India to predict the future production and also to forecast the variable of interest based on the past values of variable by using Auto Regressive Model.

Abstract: In this article, we have consider stratified random sampling scheme for the estimation of a family of general population parameters using auxiliary information in the presence of measurement errors. The general results are applied to estimate the coefficient of variation of the study variable under measurement error aspects. The optimal conditions are obtained under large sample approximation and the situations are identified for which the proposed class of estimator would be better than existing estimators. Monte-Carlo simulation study has been carried out to demonstrate the performance of proposed estimator.

Keywords : Stratified Sampling , study variate, auxiliary variate, measurement error, coefficient of variation, bias and mean square error.

Abstract: India has emerged as one of the fastest growing economy in the world with a GDP growth of 7.1 % in 2016. Due to various political and social factors the year 2016 has seen many changes in the Indian economy.

This project aims to identify the irregularities in the market by analysing the nifty 50 index, gold bullion rates and EURO–INR exchange rate day wise for the year 2016. Statistical Quality Control (SQC) is a tool used to monitor, control and improve the quality of manufacturing process by means of statistical methods. In this project the SQC techniques are implemented on economic data. The control techniques, X- bar chart, R chart and CUSUM chart were used for analysing the data. The day wise data collected was grouped into weekly data samples. The irregularities in these samples were associated with the economic and political scenarios. The analysis performed gave insight into how the major indicators of the economy were affected by various economic and political factors.

The analysis can be further extended to other economic factors and thus can become a tool to understand how the economic indicators react to economic and political situation in our country.

Abstract: This article considers the problem of estimation of coefficient of dispersion of a study variable in the light of known value of the coefficient of dispersion of an auxiliary variable. The expression for bias and mean square error of the proposed estimator has been obtained. Theoretical comparison has been made with some other existing estimators. The performance of the proposed estimator over other existing estimators considered in the article is verified with help of a simulation study.

Abstract: The Logistic and Gompertz function is a popular method for creating the experimental growth curve of tumors. The interrelation between Logistic and Gompertz model is very useful in the application of tumor and cancer cell growth model. This paper proposes a comparison between Logistic growth model and Gompertz growth model based on parameter of models. Drawing the curve between models are provided to interpret the interrelation between these growth models and their applications in Mathematical Biology.

Reference: [1] Franses, P.H.; FITTING A GOMPERTZ CURVE, journal of the operation research society, 45, 109-113(1994). [2] C. P. Winsor; THE GOMPERTZ CURVE AS A GROWTH CURVE; proceedings of the national academy of sciences, volume 18, Number 1. [3] Laird AK; DYNAMICS OF TUMOR GROWTH; British journal of cancer, 1964:18: 490-502. [4] Franses, P.H.; A METHOD TO SELECT BETWEEN GOMPERTZ AND LOGISTIC TREND CURVE. Technological forecasting and social change 46 (1994) 45-49. [5] C.P. Caldernon, T.A. Kwembe, MODELING TUMOR GROWTH, Math. Biosci. 103(1991).

Abstract: Bayesian Analysis of Some Cumulative Damage Models.

Rijji Sen and S. K. Upadhyay

A system placed under the influence of a steadily increasing stress, fails, once the cumulative effect of the resulting damage exceeds its intrinsic strength. Statistically speaking, there are two random variables X and Y, one representing the stress and the other the strength. The resulting survival probabilities are talked in terms of P(X < Y). Considering a Gaussian assumption for the strength of the system and a large sample approximation for the stepwise accumulating damage, we consider a set of models emerging from it. Bayesian analysis of these models have been carried out using some sample based approaches.

Abstract: Internet usage refers to the number of people who use internet. About 48% of the world’s population uses the internet and is increasing tremendously over the years. In 2015, the International Telecommunication Union estimated that almost half of the world’s population would be online by the end of the year. Asia has occupied the top chair in internet usage since 48.4% of internet users are from Asia.

This study analyses the internet users of the Asian countries like China, India, Indonesia, Thailand and Malaysia during the years 2000 to 2015 and predicts the internet usage in these countries in the future.

The statistical techniques like logistic and multiple regressions were employed for the prediction. The analysis performed also gives sense to how the growth of internet users is affected by various factors like age, literacy rate and Per-capita Income.

Through Linear Regression Analysis the rate of growth of internet users was found to be the highest in China and the lowest in Indonesia. Until 2015 Malaysia had the highest number of internet users but it was predicted that China with its highest rate of growth would occupy the top chair in internet usage in the upcoming years.

Abstract: In this paper we analyses State crime data which consists some major crime reported by the police for the period-2015.The crime consist of murder, rape, robbery, auto theft and so on. In this paper we use principal component analysis and correlation was used to reduce the dimensionality of the data and to know those variables that were crime prone in the study region. Using PCA, we have to maximize the variance of a linear combination of the variable. Data of crime were taken from State Crime record Bureu, Uttar Pradesh police for the year-2015.