Statistics

This paper investigates a two multi-component unit parallel system model with imperfect detection and common cause failure. A single repair facility is always available with the system but whenever a regular detector fails in detection of the failure cause, then the unit goes for replacement for which a single replacement facility is always available. Using regenerative point technique various measure of system effectiveness are obtained. The behaviour of MTSF and profit function have been studied in a particular case.

The present paper deals with estimation of the population mean of the study variable when the information on the auxiliary variable is known and their population parameters are known. In the past, a number of modified ratio estimators are suggested with known values for the Co-efficient of Variation, Co-efficient of Kurtosis, Co-efficient of Skewness, Population Correlation Coefficient etc. However all these modified ratio estimators are biased but with less mean squared errors compared to the usual ratio estimator. In this paper some strategies have been suggested to improve the performance of the existing modified ratio estimators, which lead to a class of almost unbiased modified ratio estimators; and their performances are better than the modified ratio estimators. These are explained with the help of numerical examples.

Sanitation generally refers to principles, practices, provisions, or services related to cleanliness and hygiene in personal and public life for the protection and promotion of human health and well being and breaking the cycle of disease or illness. It is also related to the principles and practices relating to the collection, treatment, removal or disposal of human excreta, household waste water and other pollutants. In this paper a study have been performed to describe the status of sanitation in U.P. and it is comprises with the Sanitation status of India. For the above purposes secondary data from Tables on Houses, Household Amenities and Assets of the Census 2001 and Census 2011, data by the Ministry of Drinking Water and Sanitation, Swacha Bharat Mission (Gramin), Baseline Survey-2012 and some facts and figures given UNICEF and WHO have been used for the fulfilment of the need. Analysis of the data has been performed for both at all India level and State level (Uttar Pradesh) level especially.

In this paper an attempt has been made to study the efficiency of randomized block designs with two missing values. Consequently, we have obtained explicit expressions for the variances of the elementary treatment contrasts, average variance and the loss of efficiency in randomized block designs due to two missing values. Further we have also tabulated the loss of efficiency for various values of and where are respectively representing the number of treatments and the number of blocks in the randomized block designs.

A step-by-step analysis of means (ANOM) procedure has been extended to analyze the data from orthogonal array experiments. The procedure is also illustrated with the help of a numerical example.

In this study, a comparison of performance among four different methods (Probability Weighted Moments (PWM), Maximum Likelihood Methods (MLM), the Methods of Moments (MOM), and the least Square Method (LSM)) of estimating the parameters of the Weibull distribution was done, using different values of ? and ?. This study contains two different experiments; experiment I and experiment II. Values of ? > ?, ? < ?, ? = ? were used in experiment I, and another varied values of ? < ?, ? < ?, ? = ? in line with some modeled distribution of the Weibull distribution, were used in experiment II. These values were generated by simulation. The aim is to find the best methods of estimating the two-parameter Weibull distribution. Based on the sample sizes and parameters considered, the method which gave the best estimate for the two-parameter Weibull distribution, is the method of Moments (MOM), taking into consideration the total deviation as a measurement for comparison. This study will help to estimate parameters associated with various models of a component or system such as reliability problems, maintainability and predictions such as MTTF, MTTFF, MTTR, MTBF, Hazard Rate etc.

In the present paper the system considered consists of two subsystems A and B. Subsystem A consists of identical operating and warm standby units. While subsystem B has two dissimilar units: main unit and a unit in cold standby. Main unit of subsystem B is assumed to be more efficient than the standby unit so when the main unit fails the system goes to the state of low efficiency. Main unit is connected to cold standby unit with a switching over device. Further, whenever there is a failure in one of the units of A and in the main unit of subsystem B, the system goes to critical state where system has to stop functioning to avoid the further failures. Also we have considered that the company providing repair facility has appointed a repairman. The repairman repairs the system in case of minor failures but when the system fails completely he has to take it to the nearest service station of the company for repair. By applying Supplementary variable technique, Laplace transformations and copula methodology transition state probabilities, asymptotic behaviour, reliability, availability, M.T.T.F., cost effectiveness and sensitivity of the system have been determined. Particular cases corresponding to the situations when the standby unit of subsystem A is in cold standby and in hot standby have also been considered. At last some numerical examples have been taken to illustrate the model.

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.