Asian Journal of Probability and Statistics

We proposed a new family of distributions called the Topp Leone exponentiated-G family of distributions with two extra positive shape parameters, which generalizes and also extends the Topp Leone-G family of distributions. We derived some mathematical properties of the proposed family including explicit expressions for the quantile function, ordinary and incomplete moments, generating function and reliability. Some sub-models in the new family were discussed. The method of maximum likelihood was used to estimate the parameters of the sub-model. Further, the potentiality of the family was illustrated by fitting two real data sets to the mentioned sub-models.

This article introduces and studies a new probability distribution called “Transmuted Power Gompertz distribution”. It looks at the properties of the transmuted power Gompertz distribution. The article also estimates the four parameters of the new model using the method of maximum likelihood estimation. The article further evaluates the goodness-of-fit of the proposed distribution compared to other distributions by means of applications of the model to two real life datasets and the result show that the proposed distribution is more flexible than the fitted existing distributions.

Objectives: The study aims to develop a Bayesian multiple regression model with informative inverse gamma prior and t the model to malaria symptom dataset.
Place and Duration of Study: The study was carried out in Masinde Muliro University of Science and Technology (MMUST). The study used 300 malaria related symptom dataset obtained from Health service records of different patients (students) between the time period of 1st January, 2015 to 20th December, 2015.
Methodology: Multiple linear regression model with Bayesian parameter estimation is used. The Normal prior distribution for θ parameter and inverse gamma prior distribution for the σ2 parameter is derived. Gibbs sampler and Metropolis Hasting algorithm is used with Markov Chain Monte Carlo (MCMC) method to produce an iteration of about 102,491 with Burn-in of 2500 and thinning of 10 that resulting to eective sample size of 90000.
Results: The results shows that all the estimated posterior predictive p-values are between 0.05 and 0.95 indicating an adequate t for the individual observation of the data in the model. The results also reveals that the data values and the average distance between the data values and the mean tend to be close to each other and the estimated coeffcient of θ′s approximately 95%draws fall within each of the corresponding highest posterior density intervals.

Conclusion: Though the Least Squares method is sucient for estimating the coeffcients of the regression parameters, the Bayesian estimates recorded comparatively very small standard errors making the Bayesian method more robust in analysing symptom dataset.

As a mono-product economy, where the main export commodity is crude oil, volatility in oil prices has implications for the Nigerian economy and, in particular, exchange rate movements. The latter is particularly important due to the twin dilemma of being an oil exporting and oil-importing country, a situation that emerged in the last decade. The study examined the effects of oil price volatility, demand for foreign exchange, and external reserves on exchange rate volatility in Nigeria using monthly data over the period from May, 1989 to April 2019. Drawing from the works of Atoi [1] Having realized the potentials of an Autoregressive conditional heteroskedasticity (ARCH) model several studies have use it in modeling financial series. However, when using the ARCH model in determining the optimal lag length of variables the processes are very cumbersome. Therefore, often time users encounter problems of over parameterization. Thus, Rydberg (2016) argued that since large lag values are required in ARCH model therefore there is the need for additional parameters. Sequel to that, this research uses the ARCH-M to solve the challenges. The study reaffirms the direct link of demand for foreign exchange and oil price volatility with exchange rate movements and, therefore, recommends that demand for foreign exchange should be closely monitored and exchange rate should move in tandem with the volatility in crude oil prices bearing in mind that Nigeria remains an oil-dependent economy.

Several multivariate statistical methods are used in population genetics but there are very few studies that have revealed the strengths and weaknesses of different methods. Thus, this study aims to reveal the strengths and weaknesses of the different multivariate statistical methods used in population genetics through the world. This synthesis is carried out according to the methodology "Preferred Reporting Items for Systematic Reviews and Meta-Analyzes" (PRISMA). This study shown that various statistical methods or combination of multivariate statistical methods are used in population genetics. It emerges that there is no a priori a better method, so it is necessary to determine the method adapted to both the data collected and the research objective. This study identified the most commonly used multivariate statistical methods in genetics such as: Ordination methods (52.50%) are methods that summarize the information contained in the data matrix by minimizing wastage. This are: principal components analysis (by 32.0% of the articles), principal coordinates analysis (by 7.50% of the articles), discriminant analysis of principal component, factorial correspondence analysis, factorial discriminant analysis, factorial analysis on distance table. Clustering methods (35%) that aim to form groups of individuals that are as similar as possible, including the hierarchical ascending clustering (17.50% of articles), neighbor-joining, and Bayesian clustering model (by 15% of the articles). The analysis of the molecular variance (7.50%) which consists of studying the intra and inter-population variation and the Mantel test (5%) which aims to test the correlation between the matrix of genetic distances and other distance matrices (environmental causes of genetic variability).