This paper investigates the inverse and power Juchez distribution. Some relevant properties are studied, and the distributions can altogether model many varieties of datasets emanating from different life phenomena. And then, a generator for other generalized distributions termed Juchez-G is developed to suffice for the relevance of robust model development. Finally, IJD and PJD showed to be a better fit over both the baseline distribution and their respective counterpart distributions, with respect to the datasets used. The proposed method is interesting and the performance is superior.

This is a comparative study on mixture distribution; where the study seeks to ascertain whether higher number of k-component mixtures could result to development of models that show better fits. In the performance comparison, special consideration was given to univariate one parameter distributions derived using mixture models, and the results show that distributions of higher k-mixture components  relatively have greater propensity to exhibit better fit than the lesser mixture component distributions (k < 3).

This paper examines the application of autoregressive integrated moving average (ARIMA) model and regression model with ARIMA errors for forecasting Nigeria’s GDP. The data used in this study are collected from the official website of World Bank for the period 1990-2019. A response variable (GDP) and four predictor variables are used for the study. The ARIMA model is fitted only to the response variable, while regression with ARIMA errors is fitted on the data as a whole. The Akaike Information Criterion Corrected (AICc) was used to select the best model among the selected ARIMA models, while the best model for forecasting GDP is selected using measures of forecast accuracy. The result showed that regression with ARIMA(2,0,1) errors is the best model for forecasting Nigeria’s GDP.

In the study, some bivariate distributions were developed from mixture model offspring, using the Independent (Product) distribution approach. These developments are categorized under the IID and IInD: where the Bivariate Exponential distribution, Bivariate Lindley distribution and Bivariate Juchez distribution are constructed as IIDs; and Bivariate Exponential-Lindley distribution, Bivariate Exponential-Juchez distribution and Bivariate Lindley-Juchez distribution as (IInDs). The properties of these distributions which involve: the shape of the bivariate PDFs, moments, moment generating function, mean, covariance and coefficient of correlation, maximum likelihood estimator, reliability analysis, renewal property and probability patterns; are studied across the distributions. Finally, under renewal properties, functions are derived which can model two-dimensional queuing and renewal processes, for events where the arrival and service times are dependent.

Tuberculosis (TB) is one of the leading causes of mortality in developing countries in world. It is an airborne disease spread through inhaling. This study investigated the cases of tuberculosis at Nnamdi Azikiwe University Teaching Hospital (NAUTH) Nigeria. The TB data used in this study are secondary data sourced from NAUTH tuberculosis register from January 2005 to December 2021. This study is a retrospective cohort and time series analysis of all the cases of tuberculosis diagnosed and confirmed. The forecast methods used in this study are that of Box-Jenkins approach and Holt-Winters. Out of 395070 presumptive cases, 52311 (11.7%) were diagnosed with tuberculosis, and male had the highest rate. The age group that was most affected was the group 35-44 (24.68%). 8.4% of the tuberculosis diagnosed tested positive. ARIMA (0,0,1) (2,0,1) [12] was selected as the best model, used in forecasting tuberculosis cases for the next four years. Tuberculosis cases predicted showed that for the next four years, there will be a slight decrease.