Statistics

In today’s globalised and competitive economic environment, insurance companies are continually faced with situation of risk where decisions are taken in the face of uncertainty. The variability of claim costs and the challenge of estimating the cost of insurance at inception of the policy make it necessary for companies to frequently assess the credibility upon which pricing, valuation and other product management decisions are made. The accuracy of estimated future claim costs plays a fundamental role in determining the underwriting profit of these insurers. This study proposed an industry-wide information based experience rating in a regulated and competitive Nigeria business environment for credible underwriting and profitability. The proposed structure incorporates various initiatives for having in place reliable, up-to-date, efficient and effective statistical system such as the Marrakech Action Plan for Statistics (MAPS), General Data Dissemination System (GDDS), Partnerships in Statistics for Development in the 21st Century (PARIS21), the Reference Regional Strategic Framework for Statistical Capacity Building in Africa (RRSF), National Strategies for the Development of Statistics (NSDS) and AFRISAT. It also integrates variation in expected claim costs from insurer to insurer in the industry, variation between expected claim costs from group to group for a given insurer, and variation from insured to insured within a group. Inferences can be made about the industry’s average, companies’ average and group-specific average.

Value at Risk (VaR) is one of the most popular measures of risk associated with financial instruments. The generalized Pareto distribution (GPD) is useful in modeling values exceeding a high threshold in estimation of VaR and Expected Shortfall (ES). It has been observed that none of the existing methods for estimating parameters of GPD performs uniformly better than others (P. Z. Bermudez and S. Kotz, 2010), and even if one develops a method, it would suffer from heavy computational requirements. Recently, P.Chen et.al (2017) proposed a method of estimating parameters of GPD based on minimum distance approach and M-estimation. In literature survey it has been observed that a study on effect of outliers on estimation of parameters of GPD has not been carried out, though presence of outliers is common in financial data. In this regard this paper focuses on the effect of outliers on estimators of parameters of GPD, on estimators of VaR and estimators of ES under Peaks over Threshold (PoT) framework obtained from different methods. A simulation study is carried out to compare performances of five robust and seven non-robust methods for estimating parameters of GPD, VaR and ES in the presence of a single additive outlier under PoT set up and it is found that robust methods suggested by P.Chen et.al (2017) for estimating GPD parameters perform on par with other estimators when shape parameter k > 0 (for thin tailed distributions), in estimating VaR in presence of outlier, especially when sample size is moderately large

The level of maternal mortality is an indicator of disparity in access to appropriate health care and nutrition services throughout their life particularly during pregnancy and childbirth. National Population Policy 2000 and National Health Policy 2002 aim to reduce the Maternal Mortality Rate (MM Rate) to 100 per 100,000 live births from the current level of 400-500. Though India has made an appreciable progress in improving the overall health status of its population but it is far from satisfaction. The pace of decline of maternal mortality on has been quite low. The death of a woman during pregnancy and childbirth is not only a health issue but also a matter of social injustice and discrimination. The complications of pregnancies and the births are found to be the foremost causes of maternal deaths. This measure reflects not only the risk of maternal death per pregnancy, but also the level of fertility in a population. The fertility beyond age 35 years is risky for both women and child and it leads to miscarriage, maternal & child mortality thus the study of the fertility beyond 35 years of age is an important issue for the researchers to study the status of maternal and child health. In this paper a simple technique has been proposed to estimate the MM Rate and MM Ratio using the age specific fertility rate (ASFR) and percentage of safe delivery beyond 35 years of age respectively, keeping in view of the above fact.

There is widespread concern that the cumulative effects of the non-response that is bound to affect any long-running longitudinal study will lead to mistaken inferences about change. We focused this work on the Longitudinal Survey of Oyo town covering the existing fifteen (15) Enumeration Areas to show the patterns of response and non-response. The Surveys started in 2008 and a two-stage stratified random sampling scheme was used in selecting 750 households. Household heads were interviewed in five waves (waves 1, 2, 3, 4 and 5). We used an interviewer-administered questionnaire to collect data on the demographic characteristics of the respondents. The Response rates for waves 1 through 5 were 77.86%, 82%, 81.33%, 82% and 80.67% respectively while the non-response rates were 22.14%, 18%, 18.67%, 18%, and 19.33% respectively. The average number of visit ranges from a minimum of 1.2 in Kosobo to a maximum of 4 in Ladigbolu. The average duration of the household interview ranges between a minimum of 7.7 minutes in Monbolaje and a maximum of 18 minutes in Asipa. Finally, fieldwork lasts on average of 11.8 hour in Asipa, but only 6.6 hours in Monbolaje. The most common interview mode is the Pencil-And-Paper (face-to-face) Interview. New entry is linked to eligibility, whereas monotone attrition is mainly due to migration. Occasional responses are due to absences while that of non-responses are due to out of scope and lack of cooperation.

This paper examines the ‘O’ level mathematics themes specifically to identify the most difficult content areas in order to improve students’ achievement in mathematics. In this study, questionnaire made up of the content areas in ‘O’ level mathematics were administered in classrooms using random sample technique. The sample consists of 214 students; 102 males and 112 females of some selected Secondary schools in Nasarawa State. The respondents are all SS III students of 2012/2013 academic session. The data collected was analysed using simple arithmetic percentages. It was established that a great number of the respondents perceived Plane Geometry as the most difficult content area in “O” level mathematics and this constitute 80 (37.4%) of the 214 respondents. This is followed by 55 (25.7%) of the respondents who are of the view that Algebraic Processes is the most difficult.

Sathe, Y. S. (1977) found a new set of sharp upper and lower bounds on the variance of the UMVUE in the case of inverse sampling motivated by the fact that a close-form expression to capture the actual variance is unavailable. Sahai, Ajit (1985) improved the variance upper bound in Sathe, Y. S. (1977). This note is motivated by their papers and by their inherent desire to capture that variance possibly more closely using their set of the sharp Sahai-Sathe’s upper-and-lower bounds. It was very heartening for the authors to realize that the same is possible. In fact the seminal result achieved by the authors in this note could be used for improving the sharpness of these bounds iteratively till it pleases the one using it for the purpose of being close to the actual variance of the UMVUE in the absence of its capture in the closed-form. The achievement is briefly illustrated through a modest empirical study to bring forth the power of the proposed iterative algorithm for the aforesaid purpose.

This study investigates the effects of malaria drugs on children of different gender under the age of five in Nigeria (Umuahia in Abia State as a case study). It was carried out by applying descriptive statistical methods and Poisson log linear regression model on different malaria drugs. To achieve this, five age groups in months (<12, 12-23, 24-35, 36-47, 48-59) and gender (male and female) were used. Secondary datasets were collected from Nigeria Demographic and Health Survey (NDHS) 2013 and department of Health and Human Services, Abia State University, Uturu. The result shows that the rate of usage of all malaria drugs considered in this study is similar for all age groups. However more males than females received Artemisinin-Based Combination Therapy (ACT). The only significant difference found is between the Amodiaquine and Chloroquine, The study therefore concludes that the effect of malaria drugs is dependent on age and gender. Apart from all the main effects of all the variables being significant, there is also a statistically significant interaction between gender, age and drug, p = 0.00134. The poissson regression result predict that in the last 12months, there is a 4.9% and 6.7% increase in the number of gender and drugs respectively considered yearly with (95% CI. 0.281 to 1.678 and 0.006 to 1.033), and also a statistical significant results, P-value = 0.010 & 0.004 respectively.

In this article we express the wigner distribution function in convenient differential forms. In addition We find the temporal evolution of the distribution function for charged particles in an external magnetic field . As a special case we report the wigner function for uniform magnetic field.

The presence of missing values in air quality data is a common issue and important task to deal with it. The data was collected using automated machines which contain missing value that can cause bias result due to differences between observed and predicted data. This paper considers hourly air pollutant concentrations such as NO, NO2, CO, SO2 and meteorological variables such as AT, WS, RH at Kemaman over a four-year period. This paper discusses the performance of Multiple Linear Regression model by using different imputation methods such as mean top bottom, linear interpolation and Markov Chain Monte Carlo (MCMC). The result shows that the MCMC method to replace the missing values obtained the highest R2 (0.649) after fitting to multiple linear regression model for prediction of ozone concentrations with selected precursors. Therefore, MCMC method produced a good fit multiple linear regression for prediction of ozone concentration in this study.

This paper attempted to fit an appropriate probability density function to available crime data in Nigeria by using the Pearson System of Distribution Approach. Rising crime rates have necessitated the need to model adequately crime occurrences to enhance effective management and control. Aggregated dataset of crime rates from 1994 to 2003 were used to estimate the parameters of the selected density functions from the Pearson system and for the goodness of fit test. Results showed that the Four Parameter Gamma density function was the most suitable for the data under study. This study has revealed the potentials of probability density functions in crime prevention and control.