A New Goodness-of-Fit Test for the Two-Parameter Gamma Distribution

This paper proposes a new goodness-of-fit for the two-parameter distribution. It is based on a function of squared distances between empirical and theoretical quantiles of a set of observations being hypothesized to have come from the gamma distribution. The critical values of the proposed statistic are evaluated through extensive simulations of the unit-scaled gamma distributions and computations. The empirical powers of the statistic are obtained and compared with some well-known tests for the gamma distribution, and the results show that the proposed statistic can be recommended as a test for the gamma distribution.

Estimating the Best-Fitted Probability Distribution for Monthly Maximum Temperature at the Sylhet Station in Bangladesh

The estimation of a suitable probability model depends mainly on the features of available temperature data at a particular place. As a result, existing probability distributions must be evaluated to establish an appropriate probability model that can deliver precise temperature estimation. The study intended to estimate the best-fitted probability model for the monthly maximum temperature at the Sylhet station in Bangladesh from January 2002 to December 2012 using several statistical analyses. Ten continuous probability distributions such as Exponential, Gamma, Log-Gamma, Beta, Normal, Log-Normal, Erlang, Power Function, Rayleigh, and Weibull distributions were fitted for these tasks using the maximum likelihood technique. To determine the model’s fit to the temperature data, several goodness-of-fit tests were applied, including the Kolmogorov-Smirnov test, Anderson-Darling test, and Chi-square test. The Beta distribution is found to be the best-fitted probability distribution based on the largest overall score derived from three specified goodness-of-fit tests for the monthly maximum temperature data at the Sylhet station.

Statistical Analysis of the Factors Affecting Academic Achievement of Undergraduate Students A Case Study of Faculty of Arts and Science Kufrah -Benghazi University

This study examined the factors affecting the academic achievement of undergraduate students at the faculty of Arts and Science Kufrah -Benghazi University as a case study. This study seeks to identify and analyze some determining factors that influence students' academic achievement in the study area. Four factors namely: psychological, family, learning facilities, and economic; were considered. The sample was randomly selected from the study population. A questionnaire was administered to 240 (90 males,150 females) students as a sample of this study. The responses of the students were analyzed to meet the objectives of the study using (SPSS) and displayed in forms and tables. After collecting the required data on the variables of the study, they were encoded to be entered into the computer to extract the statistical results. Statistical methods within the Statistical Package for Social Sciences (SPSS) were used to process data obtained by the field study of the sample. To analyze the data mean difference test is used. Results of arithmetic means of the psychological, family, learning facilities, and economic factors were medium. Furthermore, there were no statistically significant differences in the factors affecting academic achievement among the participants due to some demographic factors such as gender and marital status. following recommendations were made; provide proper learning facilities to the students and also improve the environment of the faculty. Furthermore, the students would perform well if they are properly guided by both their parents and teachers.

The Effect of Weighting Data on the Goodness of Fit Indicators of the Six Sigma Structural Equation Modeling

The main core of Structural Equation Modeling (SEM) is the parameter estimation process. This process implies a variance-covariance matrix Σ that is close as possible to the sample variance-covariance matrix of data input (S). The six Sigma survey uses ordinal (rank) values from 1 to 5. There are several weighted correlation coefficients that overcome the problems of assigning equal weights to each rank and provide a locally most powerful rank test. This paper extends the SEM estimation method by adding the ordinal weighted techniques to enhance the goodness of fit indicators. A two data sets of the Six Sigma model with different statistics properties are used to investigate this idea. The weight 1.3 enhances the goodness of fit indicators with data set that has a negative skewness, and the weight 0.7 enhances the goodness of fit indicators with data set that has a positive skewness through treating the top-rankings.

Modeling the British Pound Sterling to Nigerian Naira Exchange Rate During the Covid-19 Pandemic

The British Pound Sterling (GBP) to Nigerian Naira (NGN) exchange rate has been grossly affected by the Coronavirus 2019 (Covid-19) pandemic. It has become pertinent to identify robust models that will help to cope with the variability associated with the pandemic. Many original studies found the ARIMA method to be highly useful in modeling and forecasting exchange rates. However, not much work has been done on modeling the GBP and NGN exchange rate during the covid-19 pandemic using machine learning models. This study focuses on modeling the exchange rate between the GPB and NGN during the period of the Covid-19 pandemic by adopting the process of model comparison using the Artificial Neural Network (ANN), Autoregressive Integrated Moving Average (ARIMA), and Random Forest models to obtain an optimal model and forecasts from the model. Secondary data of the GBP to NGN exchange rate within the period of the Covid-19 pandemic from exchangerate.org.uk were used. The two machine learning models (ANN and random forest) performed better than the ARIMA model. The RF, though performed well in the training set, was outperformed in the test set by the ANN model. The ANN model was chosen to model and forecast the GBP and NGN exchange rate during the Covid-19 pandemic. The predicted fall in the GBP to NGN exchange rate to 570 by December 2021 and 575 by September 2022 using the ANN model will have a huge effect on the economy of the country as the country depends largely on imported goods. The Government and policymakers must put in place structural measures that will avoid the looming crisis.

Evaluating Percentage Rotatability For The Small Box – Behnken Design

Rotatability property for the Small Box-Behnken design is discussed in this paper. This paper aimed at applying a measure of obtaining percentage rotatability on the Small Box-Behnken designs to determine if the Small Box-behnken designs are rotatable or not and investigated the extent of rotatability in terms of percentage. The factors, q, considered range from 3 to 11. The results showed that for factors q, the Small Box-Behnken design is rotatable for q = 3 factors, near rotatable for q = 4, 7 factors and not rotatable for q = 5, 6, 8, 9, 10 and 11 factors.

Data Geometry and Extreme Value Distribution

In extreme values theory, there exist two approaches about data treatment: block maxima and peaks-over-threshold (POT) methods, which take in account data over a fixed value. But, those approaches are limited. We show that if a certain geometry is modeled with stochastic graphs, probabilities computed with Generalized Extreme Value (GEV) Distribution can be deflated. In other words, taking data geometry in account change extremes distribution. Otherwise, it appears that if the density characterizing the states space of data system is uniform, and if the quantile studied is positive, then the Weibull distribution is insensitive to data geometry, when it is an area attraction, and the Fréchet distribution becomes the less inflationary.

On Mixture GARCH Models: Long, Short Memory and Application in Finance

In this work, we study the famous model of volatility; called model of conditional heteroscedastic autoregressive with mixed memory MMGARCH for modeling nonlinear time series. The MMGARCH model has two mixing components, one is a GARCH short memory and the other is GARCH long memory. the main objective of this search for finds the best model between mixtures of the models we made (long memory with long memory, short memory with short memory and short memory with long memory) Also, the existence of its stationary solution is discussed. The Monte Carlo experiments demonstrate we discovered theoretical. In addition, the empirical application of the MMGARCH model (1, 1) to the daily index DOW and NASDAQ illustrates its capabilities; we find that for the mixture between APARCH and EGARCH is superior to any other model tested because it produces the smallest errors.

Global Structure of Determining Matrices for a Class of Differential Control Systems

This paper developed and established unprecedented global results on the structure of determining matrices of generic double time-delay linear autonomous functional differential control systems, with a view to obtaining the controllability matrix associated with the rank condition for the Euclidean controllability of the system. The computational process and implementation of the controllability matrix were demonstrated on the MATLAB platform to determine the controllability disposition of a small-problem instance. Finally, the work examined the computing complexity of the determining matrices.

Fundamental Results on Determining Matrices for a Certain Class of Hereditary Systems

Three major tools are required to investigate the controllability of control systems, namely, determining matrices, index of control systems and controllability Grammian. Determining matrices are the preferred choice for autonomous control systems due to the fact that they are devoid of integral operators in their computations. This article developed the structure of certain parameter-ordered determining matrices of generic double time-delay linear autonomous functional differential control systems, with a view to obtaining the controllability matrix associated with the rank condition for Euclidean controllability of the system. Expressions for the relevant determining matrices were formulated and it was established that the determining matrices for double time-delay linear autonomous functional differential control systems do not exist if one of the time-delays is not an integer multiple of the other paving the way for the investigation of the Euclidean controllability of generic double time-delay control systems.