Statistics

Pandey (1977) considered the exponential distribution which is generally used in life testing experiment. Epstein & Sobel (1953) and Bhattacharya & Srivastava (1974) considered the censoring procedure in life testing problem. Pandey and Malik (1994) considered the improved estimator for ?2 in exponential distribution. In this paper proposed an estimator for ?2 in case of exponential distribution and studied its properties under Linex loss function.

The negative implications of rising poverty and inequality have awakened research concern in recent time due to the perceived correlation between both issues. This study was carried out with the aim of investigating the effect of the relationship between income poverty and inequality in Nigeria because few researchers have studied them together in past studies. The head count index was used to estimate the incidence of poverty while the Gini coefficient was used to estimate income inequality based on household data from a Living Standard Survey of households in Nigeria. The national estimates of the head count and Gini coefficient were 0.34 and 0.69. For the six geo-political zones, the estimates were North East (0.36, 0.81); North West (0.30, 0.76); South South (0.36, 0.66); South West (0.33, 0.63); North Central (0.24, 0.61) and South East (0.26, 0.57) respectively. The results indicated that poverty was highest in the North East (0.36) and lowest in the North Central (0.24). Also, income inequality was highest in the North East (0.81) and lowest in the South East (0.57). This study has revealed the positive correlation between poverty and inequality because results had shown that poverty was highest where inequality was also highest. Therefore to reduce poverty, efforts should be made to ensure reduction in income inequality.

In the present investigation, a linear model has been proposed which has been found very useful in growth studies wherever phenomenon exhibit asymptotic behavior. It possesses the identical properties those of Stevens’s asymptotic regression growth model i.e. it belongs to the family of convex-concave curves and has neither maxima nor minima nor a point of inflexion. Its appropriateness and utility has also been examined with the help of data sets obtained from different areas of growth studies showing asymptotic nature. It has also been compared with Stevens’s asymptotic regression model. An improvement has been shown over Stevens’s asymptotic regression model.

In this paper, we employ Multiple Linear Regression Model to fit a model of Gross Domestic Product Per Capita of Nigeria using some World Development Indicators (WDI) as explanatory variables. Data were collected from 1981 to 2013. The five WDI are OER-Official Exchange Rate (LCU Per US$, Period Average), BM-Broad Money (% of GDP), INF-Inflation, GDP deflator (Annual %), TNR-Total Natural Resources Rents (% of GDP) and FDI-Foreign Direct Investment, Net Inflows (% of GDP).At the end of the analysis it was discovered that the OER and BM are statically significant while INF, TNR and FDI are not statistically significant. The average estimated GDP per capita of Nigeria when the effect of OER, BM, INF, TNR and FDI are zero is $-360.81. Also, 1 unit increase in OER-Official Exchange Rate (LCU Per US$, Period Average) will lead to a significant increase in GDP per capita by $4.42 (4.42USD); if BM-Broad Money (% of GDP) increases by 1% then GDP per capita will increase by $25.17; if INF-Inflation, GDP deflator (Annual %) increases by 1% then GDP per capita will decrease by $0.08; if TNR-Total Natural Resources Rents (% of GDP) increases by 1% then GDP per capita will decrease by $0.63 and if FDI-Foreign Direct Investment, Net Inflows (% of GDP) increases by 1% then GDP per capita will increase by $13.52. (Note: All the estimated parameters are significant at 5% without exception). 71.1% of the total variation in GDP per capita of Nigeria can be explained by the variations in OER-Official Exchange Rate (LCU Per US$, Period Average), BM-Broad Money (% of GDP), INF-Inflation, GDP deflator (Annual %), TNR-Total Natural Resources Rents (% of GDP) and FDI-Foreign Direct Investment, Net Inflows (% of GDP) while the remaining 28.9% could be explained by other variables other than the ones used in this model.

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

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.

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.

Two problems often crop up in adaptive sampling. One, it may not be feasible to sample according to a designated sampling plan. And two, the prescribed sampling plan may result in very small selection probabilities for some units thereby giving large weights to such units in estimation. In order to ameliorate these problems, a regression procedure that combines design and model-based techniques of estimation is proposed. Adaptive sampling designs are designs in which additional units or sites for observation are selected depending on the interpretation of observations made during initial sampling. Additional sampling is driven by the observed results from an initial sample. The results from this study demonstrate that the existing Horvitz-Thompson estimator for adaptive cluster sampling can be improved using model assistance.

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.

The paper considered the construction of a family of BIBDs using potential Lotto Designs (LDs) earlier derived from qualifying parent BIBDs. We utilized Li’s condition, to determine the qualification of a parent BIBD as LD constrained on and then considered the case since is the smallest number of tickets that can guarantee a win in a lottery. The BIBD was used as the parent BIBD for the procedure. This BIBD yielded three potential LDs each of which was completely generated using a Microsoft Office Access database computer program and their properties were studied. The three LDs, after their complete generation, yielded the and BIBDs. These BIBDs follow the generalization where are the parameters of the BIBD. A MATLAB program was used to generate a family of the BIBDs for with these new set of parameters. All the BIBDs in this family are unreduced designs.