Statistics

In this paper, we propose Bayes estimator of parameter of exponential distri¬bution Under General Entropy Loss Function (GELF) for Progressive Type-II censored data with random scheme. The proposed estimator has been com¬pared with corresponding Bayes estimator under Square Error Loss Function (SELF) and Maximum Likelihood Estimator (MLE) in terms of their risks based on simulated samples from exponential distribution.

Acceptance sampling plans developed relating to groups of items on testers are called the group acceptance sampling plan (GASP). In this scheme, a sample of items is distributed into different groups and a lot of product is rejected if more than a specified number of failures are recorded in any group. A group ac¬ceptance sampling schedule can be used to save the time and cost in inspection as compared with classical acceptance sampling. In this paper, a procedure for constructing a group acceptance sampling plan (GASP) indexed through indifference quality level (IQL) and Inverse Rayleigh distribution is proposed. Suitable tables and examples are also provided for easy selection of the plans.

This paper proposed a modified ratio-cum-product estimators of finite population mean using information on coefficient of variation and co-efficient of kurtosis of auxiliary variable in Stratified Ranked Set Sampling (SRSS). It has been shown that this method is highly beneficial to the estimation based on Stratified Simple Random Sampling (SSRS). The bias and mean squared error of the proposed estimators are derived. Theoretically, it is shown that these suggested estimators are more efficient than the estimators in Stratified simple random sampling. The results have been illustrated by numerical examples.

A dynamic graphical display among the set of independent variables (partial regression plot), tolerance value, variance inflation factor (VIF) and pair wise correlation matrix among the set of predictors offers a variety of measures for assessing the problem of colinearity and multicollinearity in a multiple regression diagnostics. Multicollinearity is a violation of one of the assumption of regression analysis. Many diagnostics measures have been proposed for detecting multicollinearity. A tolerance value of less than 0.10 or 0.20 which is equivalent to a VIF of 5 or 10, p value>0.05 and the pair-wise correlation showing a linear dependence of 0.90 and above. A transformation is carried out to remove the problem of multicollinearity and the removal will help to improve on the model (yi = b0 +b ₁X₁ + b₂X₂ +……+ b_kX_k, improve coefficient of determination (r²) and validate any of the assumption of regression analysis of homocesdasticity, linearity, normality and independence of the observations. Examples using stimulated small data sets illustrate this approach

Malaria is one of the most severe problems faced by the world even today. The objective of the present report was to make a comparative epidemiological study for the year 2009 and 2010 of malaria endemic blocks of Lakhimpur district of Assam, India to assess the malaria situation. The data have been collected from all block PHC’s under Lakhimpur district. Form the report of malaria cases for 2000-2011, Plasmodium vivax was the predominant parasite species except 2011 where Plasmodium falciparum was the majority parasite. Comparatively we got lowest API and SFR for the year 2010 than 2009. Amongst PHC’s, we saw that the Boginadi PHC, which is a tribal dominated and share border with Arunachal Pradesh, was worse affected by malaria incidence. It was observed that PHC’s sharing interstate border had many more cases compared to those having sharing inter district border. Also we got high malaria cases in foothill/forest fringe areas, where health infrastructure/health awareness is weak and transmission of the disease is high.

In multivariate sampling, the major interest is on the problem of estimation of several population characteristics which often make conflicting demands on the sampling procedure. In this type of survey, the best allocation for one item may not in general be the best for another. There is the need to come up with compromise solution in a survey with many characteristics under study. This paper focuses on comparing some techniques of optimum sample allocation which are Yates/Chatterjee, Booth and Sedransk and Vector Maximum Criterion (VMC) on five sets of real life data stratified into six strata and two variates with desired variances using: (i.) Method of maximum variances with fixed n and (ii.) arbitrary fixing of variances. The stratum sample size nh among the classes are obtained to ascertain the criterion that will produce the smallest n. Based on the set of data collected and used for the empirical study it was discovered that Vector Maximum Criterion (VMC), Booth and Sedransk are superior to Yates/Chatterjee.

In this paper, the motivation has been to give new explicit expressions for the stationary distribution of the buffer content for a fluid queue driven by an M/M/1 queue. The expressions of the buffer content distribution is derived in terms of modified Bessel functions. Finally, numerical assessment is presented to visualize the buffer content distribution.

Successive sampling is used repeatedly to survey a population over time. It allows the first sample to be taken (on the first occasion) and a second sample is then taken (on the second occasion). The scheme provides an opportunity of making use of the information obtained in the first sample in improving on the precision of future estimate. In this study, double sampling for regression estimation was used to determine the current estimate of the mean, minimum variance, maximum precision, estimate of change between the two successive occasions under consideration and estimate of average over the period of the two occasions. The data used were based on students’ enrolment in Oyo state public secondary schools and The data were collected from Planning, Research and Statistics Unit, Oyo State Ministry of Education.The current estimates for the student enrolments in Junior and Senior Secondary Schools were found to be 6,372 and 4,925 students respectively. The variances for the current estimate is more precise when ? approaches unity. Sensitivities increased for both the Junior and Senior secondary schools at 0.7 ? ? ? 1.0. The changes in current estimates between the first and second occasion were found to be -110 and -210 for Junior and Senior Secondary Schools respectively. The negative sign shows that there was decreased in number of the students enrolment in both Junior and Senior Secondary Schools in the current year compared with the previous year. Sensitivity was more in µ? for ? ? 0.32 and in ? for > 0.9225 and > 0.7385 for Junior and Senior Secondary Schools respectively. The estimate of average over time for the student’s enrolment in Junior and Senior Secondary were found to be 12, 823 students and 10,063 students respectively. The gain in information changing from one occasion to the next was 238.98% for junior category and 45.37% for Senior Category.

The main source of the Nigerian energy generation is the non-renewable source (which includes the burning of Fossil fuels). Fossil fuels (Coal, Natural gas and Petroleum) are being consumed and certain chemical compounds such as CO2 are emitted into the atmosphere. The objective of this research is to examine the trend of CO2 emission from the consumption of Fossil fuels and fitting a model for monitoring the process. Vector Autoregressive Model (VAR) was developed. The Portmanteau test for serial correlation and the Wald test for Granger-causality were carried out. VAR (1) fit the data. The Portmanteau test showed that error term are serially uncorrelated. The Wald test, showed that CO2 emission from Coal Granger-cause emission from Natural gas and Petroleum and vice-versa. The emission from Natural gas does not Granger-cause emission from Petroleum.

Mathematical software (R-software) plays major role to develop science and technology in this world. In this papers we discuss about the correlation with the help of secondary data (Pima) is collected from 784 women.