Partially accelerated life tests are very important in life testing experiments because it saves the testing time a lot of manpower, material sources and money. Partially accelerated life tests are used when the data obtained from accelerated life tests cannot be extrapolated to usual use conditions. In this paper, step stress-partially accelerated life test is discussed based on Type II censored samples when the lifetime of items under usual use condition has Topp Leone-inverted Kumaraswamy distribution. The maximum likelihood estimators for the unknown parameters and the acceleration factor are obtained. Numerical study and some interesting comparisons are presented to illustrate the theoretical results. Also, two real data sets are applied to confirm the applicability in real life.

KEYWORDS: Topp Leone-inverted Kumaraswamy distribution; censored samples; asymptotic Fisher information matrix; step stress-partially accelerated life test.

In this research daily crude oil data from U.S, Energy Information Administration from 2000-2019 is explored to test the forecasting accuracy by drawing the comparison between multiple models. Forecasting models discussed in the research cover regression, artificial neural network (ANN), exponential smoothing (ES), and autoregressive integrated moving average (ARIMA). We primarily aim to determine which mode provides the optimal forecasting results for WTI and Brent market, two major international light oil markets. The data is split into training, validation, and testing parts, with different purposes of modelling. Based on the adopted evaluation metrics, ARIMA model exhibits the optimal performance in validation data for both markets; while seasonal exponential smoothing model achieves the best 10-day and 20-day ahead forecasting.

Keywords: Crude Oil Forecasting; Regression; Neural Networks; Exponential Smoothing; ARIMA;

The unprecedented COVID-19 epidemic has put the world in peril and shifted the global landscape in unanticipated ways. Using the GARCH distribution, this study investigates the impact of the post-COVID-19 pandemic on the performance of the Nigeria Stock Exchange (NSE) index return from January 2016 to April 2022. The ARCH effect statistic utilizing the ADF statistic reveals the presence of heteroscedasticity, while the stationarity statistic indicates that data is stationary without transformation. The volatility models were found to be statistically significant, with probability values of 0.01 for the distributions. The results reveal that GARCH (1, 1) with a normal error distributions outperforms other volatility models and error distributions, and has the lowest AIC. The normal error distribution outperforms the student t and generalized error distributions in term of best fit. Furthermore, the whole sample forecast reviews that the NSE return is stable but volatile. Volatility is likely to occur in the first four months of the year 2022, while the estimate on a smaller sample size is also stable with volatility slows toward April 2022.

KEYWORDS: COVID -19, Error distributions, Forecast, Stock exchange, Volatility models.

In this study, we introduce a novel trigonometric model known as the Modified Arctan Exponential distribution. This model is created by compounding the Cauchy family of distributions with the exponential distribution serving as the baseline distribution. Our aim is to use this model for analyzing lifetime data. We have derived mathematical expressions for various statistical functions, including the probability density function, distribution function, survival function, quantile function, hazard rate function, reversed hazard rate function, cumulative hazard rate function, skewness, and kurtosis. In addition, we have provided visual representations of the probability density and hazard rate curves. The COVID-19 second wave data in Nepal were collected from May 1, 2021, to September 30, 2021, as provided by Worldometer, World Health Organization (WHO). To assess the effectiveness of our proposed model, we applied it to a dataset concerning the second wave of COVID-19 cases in Nepal. We estimated the model parameters using three distinct techniques: maximum likelihood, least squares, and Cramer’s-von Mises. To validate the model, we employed a range of statistical criteria, including Akaike’s Information Criterion, Bayesian Information Criterion, Corrected Akaike’s Information Criterion, and Hannan-Quinn Information Criterion.We also used P-P and Q-Q plots for validation purposes. To gauge the goodness of fit of our model to the data, we conducted the Kolmogorov-Smirnov, Anderson-Darling, and Cramer-von Mises tests. These tests were carried out to assess whether our model is suitable for analyzing the provided data. Our empirical findings demonstrate that, when compared to alternative lifetime distributions, our suggested distribution not only provides a better fit but also offers increased flexibility for the analysis of lifetime data. All numerical calculations were made using the R programming language.

KEYWORDS: Cauchy family of distribution, COVID-19, Exponential distribution, hazard rate function, Maximum Likelihood Estimation, Second wave.

Prediction of future observations is an important problem in many practical applications. This paper focuses on considering one-sample and two-sample prediction (as a special case of the multi-sample prediction) for a future observation from additive flexible Weibull extension-Lomax distribution. Non-Bayesian and Bayesian prediction based on Type II censoring scheme are studied. The conditional prediction approach is discussed as a non-Bayesian prediction method. Also, Bayesian

prediction is obtained under two different loss functions, the squared error and linearexponential loss functions. Moreover, a simulation study is conducted to evaluate the performance of the derived predictors and three applications of COVID -19 data in some countries are considered.

KEYWORDS: Additive flexible Weibull extension-Lomax distribution, one-sample prediction, two-sample prediction, conditional prediction approach, Bayesian prediction, squared error loss function, linear-exponential loss function.

This paper estimates the dynamic random effect probit models and endogeneous switching regression using the Ugandan household panel survey. After controlling for observed and unobserved differences in individual characteristics, the paper still finds strong evidence of state dependence, which is that past poverty increases the risk of future poverty. In the presence of genuine state dependence, short run polices are more effective. It is of important to keep households not to fall into poverty in the first place. Otherwise, they are more likely to develop unfavorable (poverty induced behaviors) attitudes that precipitate the chance being in an extended poverty. Hence, targeting households whose consumption is slightly above the poverty line using short term financial instruments (credit and insurance service) can be a viable option. In the transition probability model, the impact of an explanatory variable switches depending on whether an individual is poor or not in the previous round. Education, large proportion of adult household members and having electronic device such as TV-radio always reduce the incidence of poverty. They keep individuals from falling into poverty in the first place and/or assists them to escape poverty. On the other hand, being married, drought and the incidence of civil strife increase both the poverty persistence as well as poverty entry probabilities.

KEYWORDS: Poverty, state-dependence, dynamic models, attrition, Uganda.