##### Definite Probabilities from Division of Zero by Itself Perspective

Wangui Patrick Mwangi

Asian Journal of Probability and Statistics, Page 1-26
DOI: 10.9734/ajpas/2020/v6i230155

Over the years, the issues surrounding the division of zero by itself remained a mystery until year 2018 when the mystery was solved in numerous ways. Afterwards, the same solutions provided opened many other doors in academic space and one of the applications is in sure probabilities. This research is all about the sure probabilities computed from the zero divided by itself point of view. The solutions obtained in the computations are in harmony with logic and basic knowledge. A wide range of already existing probability distribution functions has been applied in different scenarios to compute the sure probabilities unanimously and new findings have also been encountered along the way. Some of the discrete and continuous probability distribution functions involved are the binomial, hypergeometric, negative binomial, Poisson, normal and exponential among others. It has been found in this work that sure probabilities can be evaluated from the division of zero by itself perspective. Another new finding is that in case of combinatorial, if the numerator is smaller than the denominator, then the solutions tend to zero when knowledge in gamma functions, integrations and factorials is applied. Again, if the case of continuous pdf involves integration and random variable specified in the direction of the parameter, then indirect computation of such probabilities should be applied. Finally, it has been found that the expansion of the domains of some of the parameters in some existing probability distribution functions can be considered and the restriction in conditional probabilities can be revised.

##### The Beta Type I Generalized Half Logistic Distribution: Properties and Application

P. O. Awodutire, E. C. Nduka, M. A. Ijomah

Asian Journal of Probability and Statistics, Page 27-41
DOI: 10.9734/ajpas/2020/v6i230156

In a view to obtain a new distribution that is more exible than the type I generalized half logistic distribution, we used the beta-G generator and the type I generalized half logistic distribution. Some properties of the new distribution including the cummulative distribution function,survival function, hazard function were studied. Estimation of parameters were done using the maximum likelihood estimation method. Application of the derived distribution to lifetime data was illustrated by applying to remission times of bladder cancer patient data and survival times of guinea pigs.

##### Analysis of ARIMA-Artificial Neural Network Hybrid Model in Forecasting of Stock Market Returns

Yakubu Musa, Stephen Joshua

Asian Journal of Probability and Statistics, Page 42-53
DOI: 10.9734/ajpas/2020/v6i230157

This study focuses on the modelling of Nigerian stock market all–shares index and evaluations of predictions ability using ARIMA, Artificial Neural Network and a hybrid ARIMA-Artificial Neural Network model. The ARIMA (1,1,1) model and neural network with architecture (6:1:3) turns out to be the most fitted among the considered models, these models were used for forecasting the returns, and their performances have been compared according to some statistical measure of accuracy. A hybrid model has been constructed using ARIMA-Artificial Neural Networks model, the computational results on the data reveal that the hybrid model using Artificial Neural Network, provides better forecasts, and will enhance forecasting over the single ARIMA and Artificial Neural Networks models. The study recommends the use of ARIMA-Artificial neural network for modelling and forecasting stock market returns.

##### ARIMA Modelling of Neonatal Mortality in Abia State of Nigeria

C. Nwokike, Chukwudike, C. Offorha, Bright, Obubu Maxwell, O. Uche-Ikonne, Okezie, C. Onwuegbulam, Chisom

Asian Journal of Probability and Statistics, Page 54-62
DOI: 10.9734/ajpas/2020/v6i230158

In this study, the incidence neonatal mortality in Abia State of Nigeria was considered
using data from January 2014 to December 2018. The data was obtained from the Federal
Medical Centre, Umuahia in Abia State of Nigeria. The time plot of the data and the ADF
test conducted conrmed the series to be stationary. The plots of the ACF and PACF cut
o after lags 4 and 1 respectively which suggested ARIMA (1, 0, 4). However, diagnostic
checks led us to select ARIMA (1, 0, 1) as the best model to t the data and it was used to
make forecast. Our forecasted values indicate there will be a continous decline in the incidence
of neonatal mortality in Abia State of Nigeria. Much should be done to even expedite the decrease.