Open Access Original Research Article

Comparison of Different Parametric Methods in Handling Critical Multicollinearity: Monte Carlo Simulation Study

Obubu Maxwell, C. Nwokike Chukwudike, O. Virtus Chinedu, C. Okoye Valentine, Obite Chukwudi Paul

Asian Journal of Probability and Statistics, Page 1-16
DOI: 10.9734/ajpas/2019/v3i230085

In regression analysis, it is relatively necessary to have a correlation between the response and explanatory variables, but having correlations amongst explanatory variables is something undesired. This paper focuses on five methodologies for handling critical multicollinearity, they include: Partial Least Square Regression (PLSR), Ridge Regression (RR), Ordinary Least Square Regression (OLS), Least Absolute Shrinkage and Selector Operator (LASSO) Regression, and the Principal Component Analysis (PCA). Monte Carlo Simulations comparing the methods was carried out with the sample size greater than or equal to the levels  considered in most cases, the Average Mean Square Error (AMSE) and Akaike Information Criterion (AIC) values were computed. The result shows that PCR is the most superior and more efficient in handling critical multicollinearity problems, having the lowest AMSE and AIC values for all the sample sizes and different levels considered.

Open Access Original Research Article

Analysis and Modelling of Extreme Rainfall: A Case Study for Dodoma, Tanzania

Emmanuel Iyamuremye, Samson W. Wanyonyi, Drinold A. Mbete

Asian Journal of Probability and Statistics, Page 1-29
DOI: 10.9734/ajpas/2019/v3i230086

The analysis of climate change, climate variability and their extremes has become more important as they clearly affect the human society and ecology. The impact of climate change is reflected by the change of frequency, duration and intensity of climate extreme events in the environment and on the economic activities. Climate extreme events, such as extreme rainfall threaten to environment, agricultural production and loss of people’s lives. Dodoma daily rainfall data exported from R-Instat software were used after being provided by Tanzania Meteorological Agency. The data were recorded from 1935 to 2011. In this essay, we used climate indices of rainfall to analyse changes in extreme rainfall. We only used 6 rainfall indices related to extremes to describe the change in rainfall extremes. Extreme rainfall indices did not show statistical evidence of a linear trend in Dodoma rainfall extremes for 77 years. Apart from the extreme rainfall indices, this essay utilized two techniques in extreme value theory namely the block maxima approach and peak over threshold approach. The two extreme value approaches were used for univariate sequences of independent identically distributed (iid) random variables. Using Dodomadaily rainfall data, this essay illustrated the power of the extreme value distributions in modelling of extreme rainfall. Annual maxima of Dodoma daily rainfall from 1935 to 2011 were fitted to the Generalized Extreme Value (GEV) model. Gumbel was found to be the best fit of the data after likelihood ratio test of GEV and Gumbel models. The Gumbel model parameters were considered to be stationary and non-stationary in two different models. The stationary Gumbel model was found to be good fit of Dodoma maximum rainfall. Later, the levels at which maximum Dodoma rainfall is expected to exceed once, on average, in a given period of time T = 2, 5, 10, 20, 30, 50 and 100 years, were obtained using stationary Gumbel model. Lastly, the data of exceedances were fitted to     the Generalized Pareto (GP) model under stationary climate assumption.

Open Access Original Research Article

Fitting Probability Distribution Function to Malaria Incidence Data

Drinold Mbete, Kennedy Nyongesa, Joseph Rotich

Asian Journal of Probability and Statistics, Page 1-12
DOI: 10.9734/ajpas/2019/v3i230087

Abstract: Malaria remains a major infectious disease that affects millions of people. Once infected with Plasmodium parasites, a host can develop a broad range of clinical presentations, which result from complex interactions between factors derived from the host, the parasite and the environment. Malaria has historically been a very serious health problem and currently poses the most significant threat to the health of Masinde Muliro University of Science and Technology students, data shows that more than 70% percent of pediatric cases are due to malaria.

Methodology: Hence, the study aimed to fit malaria incidences dataset for the period 1st January, 2013 to 31st December, 2015. Data on monthly malaria incidence was obtained from the Masinde Muliro University of Science and Technology health service. Gamma, Weibull and Lognormal Distributions were employed to fit the malaria incidence dataset using R-software.

Results: High malaria incidences were observed in the months of August, September and November. AIC values results showed that lognormal distribution had the lowest AIC value of 185.9875 followed by the Gamma distribution with a value of 187.8815 and then the Weibull distribution with a value of 188.7271. This confirmed the lognormal distribution to be the best fitting distribution for the malaria incidence dataset

Conclusion: The Poisson regression model did not accurately fit the data on malaria incidences due to over dispersion in the data but lognormal distribution was a better fit compared to gamma and Weibull distribution.

Open Access Original Research Article

Modeling Volatility of Asset and Volume of Trade Returns in the Nigerian Stock Market in the Presence of Random Level Shifts

David Adugh Kuhe, Moses Abanyam Chiawa, Sylvester Chigozie Nwaosu, Jonathan Atsua Ikughur

Asian Journal of Probability and Statistics, Page 1-25
DOI: 10.9734/ajpas/2019/v3i230091

This study investigated the impact of volatility shock persistence on the conditional variance in the Nigerian stock returns using symmetric and asymmetric higher order GARCH family models in the presence of random level shifts and non-Gaussian errors. The study utilised Bai and Perron methodology to detect structural breakpoints in the conditional variance of daily stock and volume of trade returns in the Nigerian stock market from 2nd January, 1998 to 22nd March, 2017. The study employed symmetric GARCH (3,2) and GARCH (2,1)-M models to estimate volatility of asset returns, symmetric GARCH (2,2) and GARCH (2,1)-M to model volatility of volume of trade returns and asymmetric EGARCH (2,2), TGARCH (3,2) and PGARCH (2,3) models to measure the volatility of asset returns as well as asymmetric EGARCH (2,1), TGARCH (1,3) and PGARCH (3,2) models to estimate volatility of volume of trade returns. These models were optimally selected using information criteria and log likelihood as the best fitting symmetric and asymmetric GARCH models to estimate the conditional volatility of asset and volume of trade returns in the Nigerian stock market with and without structural breaks. Results revealed that when random level shifts were ignored in volatility models, the shocks persistence were very high with long memory and variance explosion. But when the random level shifts were incorporated into the GARCH models, there was a significant reduction in the volatility shocks persistence and long memory. Moreover, volatility half-lives also declined drastically while accounting for these sudden level shifts in variance. The study found asymmetry without leverage effects as well as a positive risk-return tradeoff for both asset and volume of trade returns in the Nigerian stock market. The Nigeria banking reform of 2004, the Global Financial and Economic Crises, as well as other local events in Nigeria, were found to have negative and significant impacts on the Nigerian stock market. The study provided some policy recommendations.

Open Access Original Research Article

On Properties and Applications of Lomax-Gompertz Distribution

A. Omale, O. E. Asiribo, A. Yahaya

Asian Journal of Probability and Statistics, Page 1-17
DOI: 10.9734/ajpas/2019/v3i230092

This article introduces a new distribution called the Lomax-Gompertz distribution developed through a Lomax Generator proposed in an earlier study. Some statistical properties of the proposed distribution comprising moments, moment generating function, characteristics function, quantile function and the distribution of order statistics were derived. The plots of the probability density function revealed that it is positively skewed. The model parameters have been estimated using the method of maximum likelihood. The plot the of survival function indicates that the Lomax-Gompertz distribution could be used to model time or age-dependent data, where probability of survival is believed to be  decreasing  with time or age. The performance of the Lomax-Gompertz distribution has been compared to other generalizations of the Gompertz distribution using three real-life datasets used in earlier researches.