Statistics

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.

Many researchers have carried out research on students’ academic performances in the University system, but there is dearth of information about models which focus on the relationship between students pre and post admission performances. This paper was therefore designed to model relationship between students’ pre and post admission performances. Information on pre admission performances (Olevel, Jamb and Post-Jamb results) and post-admission performances (100L – 400L results) of students’ in Statistics Department, Federal University of Agriculture, Abeokuta, Ogun State, Nigeria was collected from students’ file. Correlation matrix and Canonical Correlation analysis were used to know the degree of relationship that exists between the pre and post admission performances. The principal component analysis was employed to reduce the multidimensional data. Scree plot was used to determine the spread of the trend of the components and bi plot was used to determine the degree of closeness of the students’ pre and post admission performances. There is no relationship between pre and post admission performances. Also, no strong relationship among pre admission performances, while the relationship among post admission performances is very high. Post admission performances are highly related to students’ CGPA. The proportion of variance accounted for by the first, second and third principal Components are 50.7542%, 16.5712% and 15.6224% respectively with cumulative proportion of 82.95%. The first, second and third components are chosen. The seven components were reduced to three. Post admission performances are closely related and stand as the determinant of students’ class of degree.

In this paper, we establish some expectation identities satisfied by single and product moments of Generalized Order Statistics from Left Truncated Logistic Distribution. These identities are independent of left truncation point and therefore also applicable to Logistic as well as for half Logistic distributions studied in Balakrishnan (1985) and Saran and Pandey (2012) . A particular case of these results verify the corresponding results of Saran and Pandey (2004).

This paper aim to discuss the preliminary study of modelling algorithm setting of Stochastic Boosted Regression Trees (BRT) using R statistical software. The ground level ozone (O3) concentrations from a Malaysia’s air quality monitoring station was used as a case study. The new approach; BRT developed by Friedman (2001), Friedman (2002) and adopted by Yahaya (2013) in air pollution studies. BRT is differ substantially from traditional regression-based approaches. BRT are constructed of multiple regressions models which finally produce a single ‘best iteration’ model to optimize prediction performance. Sensitivity testing of model been carried out to determine the best parameters’ setting which are number of trees (nt) (1000-10000), learning rates (lr) (0.005-0.5), and interaction depth (tc) (1-10) to suits the ozone data. Results indicated that the BRT analysis algorithm best modeled with the best combination of parameters lr=0.001, tc=5 and nt=5301 that achieves minimum predictive error (minimum error for predictions). The algorithm model would crucially best provided clear benefit for air pollution study and their ability to model complex variable interactions and non-linear effects.

Some construction methods of 3-resolvable regular group divisible designs based on incidence matrix of known affine resolvable balanced incomplete block designs and 3-resolvable group divisible type partially balanced incomplete block designs with unequal block sizes within each resolution set based on incidence matrix of known symmetric balanced incomplete block designs are proposed with illustrations.

This paper deals with a cold standby redundant integrated h/w and s/w systems with priority, preventive maintenance, maximum operation time and maximum repair time. The system fails completely directly from normal mode. A single repair facility is provided who visits the system immediately. After, a maximum operation time system undergoes for preventive maintenance directly from normal mode. If repair of the h/w is not possible by the server up to a pre-specific time, it is replaced by new one with some replacement time. However, only up-gradation of the software by new one is made whenever s/w fails to execute the desired function properly. In model 1st, no priority is given whereas; in 2nd model, priority is given to s/w up-gradation over h/w repair. The failure time distribution of the h/w and s/w follows negative exponential while the distributions of preventive maintenance, repair, up-gradation and replacement time are taken as arbitrary with different probability density functions. The comparative study of mean time to system failure (MTSF) and profit function of both models have been made graphically with respect to preventive maintenance rate for fixed values of other parameters.

In this paper, Bayes estimator is derived for the parameter of the exponential model with presence of outliers based on records value. This estimator compared with estimator when we not use of records value.

In this paper, Bayesian estimators of the population proportion of a sensitive attribute were developed when real life data were gathered through the administration of survey questionnaires on an induced abortion on 300 matured women in some selected hospitals in the metropolis. Using both the Kumaraswamy (KUMA) and the Generalised (GLS) beta distributions as alternative beta priors, efficiency of the proposed Bayesian estimators was established for a wide interval of the values of the population proportion. We observed that for small, medium as well as large sample sizes, the proposed Bayesian estimators were better than the conventional Bayesian estimator proposed by Hussain and Shabbir [10] when a simple beta prior was used.