Open Access Original Research Article

Liming Xie

This paper is to estimate the survey for 98000 addresses from 1999-2017 in United States bureau of Census by using cluster analysis. The analysis is mainly applied by Approximate Covariance Estimation for CLUSTING (ACECLUS), and procedure variables for CLUSTING (VARCLUS) to test some important parameters such as average linkage, two-stage density linkage, Cubic Clustering Criterions (CCC), R-Square, Ward’s minimum variance techniques, as well as Tree procedure for deeper exploring the clusters or variables. After the overall analysis, the results show that there is existence of strong covariate correlation for variables X8 and X15 with respond variable Y (Mobility periods). Hence, Reason “Retired” from survey data is most important impact on mobility other than the reasons “Wanted better neighborhood or less crimes” and “Wanted cheaper housing” that are popular and highly frequent.

Open Access Original Research Article

Jeremy Becnel, Daniel Riser-Espinoza

The Radon transform maps a function on n-dimensional Euclidean space onto its integral over a hyperplane. The fields of modern computerized tomography and medical imaging are fundamentally based on the Radon transform and the computer implementation of the inversion, or reconstruction, techniques of the Radon transform. In this work we use the Radon transform with a Gaussian measure to recover random variables from their conditional expectations. We derive reconstruction algorithms for random variables of unbounded support from samples of conditional expectations and discuss the error inherent in each algorithm.

Open Access Original Research Article

Mbuba Morris Mwiti, Samson W. Wanyonyi, Davis Mwenda Marangu

The Central limit theorem is a very powerful tool in statistical inference and Mathematics in general, since it has numerous applications such as in topology and many other areas. For the case of probability theory, it states that, “given certain conditions, the sample mean of a sufficiently large number or iterates of independent random variables, each with a well-defined mean and well-defined variance, will be approximately normally distributed”. In the research paper, three different statements of our theorem (CLT) are given. This research paper has data regarding the shoe size and the gender of the of the university students. The paper is aimed at finding if the shoe sizes converges to a normal distribution as well as find the modal shoe size of university students and to apply the results of the central limit theorem to test the hypothesis if most university students put on shoe size seven. The Shoe sizes are typically treated as discretely distributed random variables, allowing the calculation of mean value and the standard deviation of the shoe sizes. The sample data which is used in this research paper belonged to different areas of Kibabii University which was divided into five strata. From two strata, a sample size of 74 respondents was drawn and from the remaining three strata, a sample of 73 students per stratum was drawn at random which totaled to a sample size of 367 respondents. By analyzing the data, using SPSS and Microsoft Excel, it was vivid that the shoe sizes are normally distributed with a well-defined mean and standard deviation. We also proved that most university students put on shoe size seven by testing our hypothesis using the p-value. The modal shoe size for university students was found to be seven since it had the highest frequency (97/367). This research was aimed at enlightening shoe investors, whose main market is the university students, on the shoe sizes that are on high demand among university students.

Open Access Original Research Article

Wiri, Leneenadogo, Tuaneh, Godwin Lebari

The study applied Autoregressive Integrated Moving Average Intervention in modelling crude oil prices in Nigeria spanning the period from January 1986 to June 2017. The time plot of the series showed an abrupt increase in the series and this called for intervention modelling. The data was divided into three set (actual series, pre-intervention and post-intervention series). The Augmented Dickey Fuller (ADF) was used to test for unit root on each of the series and were all found to be non-stationary at levels, they (actual, pre and post- intervention series) were however non stationary at first difference. Eighteen models were estimated and the best model was the pre-intervention model that minimise the Akaike information criterion (AIC) (ARIMA (111)) with AIC of (4.4.578). The plot of the residual correlogram showed adequacy of the model. The model was adequate since there was no spike that cut the level of the correlogram and the histogram of the residual was normally distributed with probability values (0.0000).

Open Access Original Research Article

S. Kuje, K. E. Lasisi

In this article, the Quadratic rank transmutation map proposed and studied by Shaw and Buckley [1] is used to construct and study a new distribution called the transmuted Lomax-Exponential distribution (*TLED*) as an extension of the Lomax-Exponential distribution recently proposed by Ieren and Kuhe [2]. Using the transmutation map, we defined the probability density function and cumulative distribution function of the transmuted Lomax-Exponential distribution. Some properties of the new distribution such as moments, moment generating function, characteristics function, quantile function, survival function, hazard function and order statistics are also studied. The estimation of the distributions’ parameters has been done using the method of maximum likelihood estimation. The performance of the proposed probability distribution is being tested in comparison with some other generalizations of Exponential distribution using a real life dataset. The results obtained show that the *TLED *performs better than the other probability distributions.