Open Access Original Research Article

Bayesian Estimation and Prediction of Discrete Gompertz Distribution

M. A. Hegazy, R. E. Abd El-Kader, A. A. El-Helbawy, G. R. Al-Dayian

Journal of Advances in Mathematics and Computer Science, Page 1-21
DOI: 10.9734/jamcs/2021/v36i230335

In this paper, Bayesian inference is used to estimate the parameters, survival, hazard and alternative hazard rate functions of discrete Gompertz distribution. The Bayes estimators are derived under squared error loss function as a symmetric loss function and linear exponential loss function as an asymmetric loss function. Credible intervals for the parameters, survival, hazard and alternative hazard rate functions are obtained. Bayesian prediction (point and interval) for future observations of discrete Gompertz distribution based on two-sample prediction are investigated. A numerical illustration is carried out to investigate the precision of the theoretical results of the Bayesian estimation and prediction on the basis of simulated and real data. Regarding the results of simulation seems to perform better when the sample size increases and the level of censoring decreases. Also, in most cases the results under the linear exponential loss function is better than the corresponding results under squared error loss function. Two real lifetime data sets are used to insure the simulated results.

Open Access Original Research Article

Symbolic Derivation of a Probability-Ready Expression for the Reliability Analysis of a Multi-State Delivery Network

Ali Muhammad Ali Rushdi, Motaz Hussain Amashah

Journal of Advances in Mathematics and Computer Science, Page 37-56
DOI: 10.9734/jamcs/2021/v36i230337

This paper deals with the reliability of a multi-state delivery network (MSDN) with multiple suppliers, transfer stations and markets (depicted as vertices), connected by branches of multi-state capacities, delivering a certain commodity or service between their end vertices. We utilize a symbolic logic expression of the network success to satisfy the market demand within budget and production capacity limitations even when subject to deterioration. This system success is a two-valued function expressed in terms of multi-valued component successes, and it has been obtained in the literature in minimal form as the disjunction of prime implicants or minimal paths of the pertinent network. The main contribution of this paper is to provide a systematic procedure for converting this minimal expression into a probability-ready expression (PRE). We successfully extrapolate the PRE concept from the two-valued logical domain to the multi-valued logical domain. This concept is of paramount importance since it allows a direct transformation of a random logical expression, on a one-to-one one, to its statistical expectation form, simply by replacing all logic variables by their statistical expectations, and also substituting arithmetic multiplication and addition for their logical counterparts (ANDing and ORing). The statistical expectation of the expression is its probability of being equal to 1, and is simply called network reliability. The proposed method is illustrated with a detailed symbolic example of a real-case study, and it produces a more precise version of the same numerical value that was obtained earlier by an alternative means. This paper is a part of an ongoing activity to develop pedagogical material for various candidate techniques for assessing multi-state reliability.

Open Access Original Research Article

An Alternative Approach to Solving Cubic and Quartic Polynomial Equations

Ababu Teklemariam Tiruneh

Journal of Advances in Mathematics and Computer Science, Page 57-72
DOI: 10.9734/jamcs/2021/v36i230338

Aims: The aim of the research study was to develop a more direct and intuitive approach for the solution of polynomial equations of degree 3 and four.

Study Design:  The study employed equivalent polynomial substitution that is more intuitive and direct to formulate than the traditional formulations and one that is easily solvable.

Place and Duration of Study: The study has been undertaken by the author at the university of Eswatini in the period from February to March 2021.

Methodology: Two alternative procedures have been presented for the analytical solution of cubic and quartic equations and demonstrated with worked examples. The solution is derived through a direct procedure without involving intermediate variable substitution.

Results: For cubic equations, the solution provides explicit expression of an equivalent cubic that is formed directly in terms of the original variable x. As such, the formula is intuitive and simple to derive or understand as well as apply. For the quartic equations, the same decomposition form is used as that of the cubic equation using two quadratic polynomials that have symmetric form thus making it easy to develop the solution as well as solve the equations

Conclusion: The alternative formula is easy to formulate and solve and provides a more intuitive basis for understanding and solving polynomial equations.

Open Access Original Research Article

Open Access Original Research Article

Oscillation Criteria for a Class of Second-Order Dierential Equation with Neutral Term

Yu-Ping Zhao, Fu Hua

Journal of Advances in Mathematics and Computer Science, Page 89-94
DOI: 10.9734/jamcs/2021/v36i230340

This paper is concerned with oscillation criteria for a class of second-order dierential equation with neutral term.We obtain sucient conditions for the oscillation of this equation by using  Riccati transformation and some analytical skill.

Open Access Original Research Article

Modelling Petroleum Prices between Garch and Intergeated Garch, (Igarch)

M. E. Archibong, I. D. Essi

Journal of Advances in Mathematics and Computer Science, Page 95-101
DOI: 10.9734/jamcs/2021/v36i230341

In this paper, the comparison of using garch (1, 1) and intergrated garch, igarch (1, 1) models on petroleum prices will be examined. This time-varying variation of asset returns as the horizon widens about kurtosis and volatility persistence are calculated and the results shows that petroleum prices dynamics submits more to igarch (1, 1) than garch (1, 1) model.

Open Access Original Research Article

Robustness of T-test Based on Skewness and Kurtosis

Steven T. Garren, Kate McGann Osborne

Journal of Advances in Mathematics and Computer Science, Page 102-110
DOI: 10.9734/jamcs/2021/v36i230342

Coverage probabilities of the two-sided one-sample t-test are simulated for some symmetric and right-skewed distributions. The symmetric distributions analyzed are Normal, Uniform, Laplace, and student-t with 5, 7, and 10 degrees of freedom. The right-skewed distributions analyzed are Exponential and Chi-square with 1, 2, and 3 degrees of freedom. Left-skewed distributions were not analyzed without loss of generality. The coverage probabilities for the symmetric distributions tend to achieve or just barely exceed the nominal values. The coverage probabilities for the skewed distributions tend to be too low, indicating high Type I error rates. Percentiles for the skewness and kurtosis statistics are simulated using Normal data. For sample sizes of 5, 10, 15 and 20 the skewness statistic does an excellent job of detecting non-Normal data, except for Uniform data. The kurtosis statistic also does an excellent job of detecting non-Normal data, including Uniform data. Examined herein are Type I error rates, but not power calculations. We nd that sample skewness is unhelpful when determining whether or not the t-test should be used, but low sample kurtosis is reason to avoid using the t-test.

Open Access Review Article