Open Access Data Article

Survey Data on Problems with Electricity Distribution in Delta State, South-South, Nigeria

Jonathan Tsetimi, Augustine Atonuje, James Mamadu

Journal of Advances in Mathematics and Computer Science, Page 1-15
DOI: 10.9734/jamcs/2021/v36i130326

The dataset presented captures both the customers’ experience and observed problems with electricity distribution in Delta State, South-South, Nigeria. The data is obtained by means of a well-structured questionnaire implemented by trained interviewers In obtaining the demographic information respondents mostly had to tick(Ö) the appropriate responses on the questionnaires. To obtain the customers’ experiences with the distribution company (DISCO), the respondents were presented with a series of positive statements and were expected to assign numbers between 1 and 5 on a five-point scale to indicate their level of agreement with the positive statements. For the observed problems with the services of the distribution company, respondents were to assign scores between 0 and 10 inclusive depending on the severity of the observed problems. The data was analysed by means of two computer software packages; Microsoft Excel, 2016 Edition and IBM SPSS Version 23. The data is presented in charts, tables, database and spreadsheet files.

Open Access Original Research Article

Bivariate Burr Type III Distribution: Estimation and Prediction

A. A. M. Mahmoud, R. M. Refaey, G. R. AL-Dayian, A. A. EL-Helbawy

Journal of Advances in Mathematics and Computer Science, Page 16-36
DOI: 10.9734/jamcs/2021/v36i130327

In this paper, a bivariate Burr Type III distribution is constructed and some of its statistical properties such as bivariate probability density function and its marginal, joint cumulative distribution and its marginal, reliability and hazard rate functions are studied. The joint probability density function and the joint cumulative distribution are given in closed forms. The joint expectation of this distribution is proposed. The maximum likelihood estimation and prediction for a future observation are derived. Also, Bayesian estimation and prediction are considered under squared error loss function. The performance of the proposed bivariate distribution is examined using a simulation study. Finally, a data set is analyzed under the proposed distribution to illustrate its flexibility for real-life application.

Open Access Original Research Article

A New Statistical Test for PRNG Based on the Attendance’s Law

Babacar Alasane Ndaw, Ousmane Ndiaye, Mamadou Sanghar´e, Cheikh Thi´ecoumba Gueye

Journal of Advances in Mathematics and Computer Science, Page 37-46
DOI: 10.9734/jamcs/2021/v36i130328

One family of the cryptographic primitives is random Number Generators (RNG) which have several applications in cryptography such that password generation, nonce generation, Initialisation vector for Stream Cipher, keystream. Recently they are also used to randomise encryption and signature schemes.

A pseudo-random number generator (PRNG) or a pseudo-random bit generator (PRBG) is a deterministic algorithm that produces numbers whose distribution is on the one hand indistinguishable from uniform ie. that the probabilities of appearance of the different symbols are equal and that these appearances are all independent. On the other hand, the next output of a PRNG must be unpredictable from all its previous outputs. Indeed, A set of statistical tests for randomness has been proposed in the literature and by NIST to evaluate the security of random(pseudo) bit or block. Unfortunately there are non-random binary streams that pass these standardized tests.

In this pap er, as outcome, we intro duce on the one hand a new statistical test in a static contextcalled attendance’s law and on the other hand a distinguisher based on this new attendance’s law.



Open Access Original Research Article

Solution of Euler’s Differential Equation and AC-Laplace Transform of Inverse Power Functions and Their Pseudofunctions, in Nonstandard Analysis

Tohru Morita

Journal of Advances in Mathematics and Computer Science, Page 47-60
DOI: 10.9734/jamcs/2021/v36i130329

It is shown that the index law of the Riemann-Liouville fractional derivative is recovered when nonstandard analysis is applied, and then the solutions of Euler’s differential equation are obtained in nonstandard analysis, where infinitesimal number appears. They are given in the form, from which the solutions in distribution theory are obtained. In the derivation, the AC-Laplace transforms of functions tν and tν(loge t) m for complex number ν and positive integer m, are used. By using these formulas, the AC-Laplace transforms of functions tn + and
tn +(loge t) m for positive integers n and m, and their pseudofunctions are obtained with the aid of nonstandard analysis.

Open Access Original Research Article

Autoregressive Modeling and Forecasts of Degema Monthly Allocation: Buy’s-Ballot and Bartlett’s Transformation

Herbert, AfeyaIbibo, Biu, Oyinebifun Emmanuel, Enegesele, Dennis, Wokoma, Dagogo Samuel Allen

Journal of Advances in Mathematics and Computer Science, Page 61-75
DOI: 10.9734/jamcs/2021/v36i130330

The paper focused on Autoregressive modeling and forecasts of Degema Local Government Council Monthly Allocation (DLGCMA) in River State, Nigeria. The Buys-Ballot table and Bartlett’s Transformation method were adopted to identify the trend pattern and to determine the best transformation for the series. The logarithmic transformation was adjudged to be the best and was applied to stabilize the variance. Identification of the trend and stationary for the data set was done and the DLGCMA series showed a linear trend that was non-stationary. The stationarity of the DLGCMA series was obtained after the first difference. The ARIMA models were fitted to the series base on the behaviour of autocorrelation function (ACF) and partial autocorrelation function (PACF). Finally, the model selection criteria called Akaike information criterion was used to determine the best model among the predicted models. The AR(3,1,0) model ( X= 0.56Xt-1 + 0.17Xt-2 + 0.64Xt-3 - 0.37Xt-4 + et) was considered to be the best model because it has the least value of the Akaike information criterion (AIC). Hence, the forecasts for the next allocation of twenty-four (24) months ahead were determined.

Open Access Original Research Article

Internal Exact Controllability of the Heat Equation in Finite Dimension by Strategic Actuators Zone

Mame Libasse Laye Ane, Cheikh Seck, Abdoulaye Sene, Mary Teuw Niane

Journal of Advances in Mathematics and Computer Science, Page 76-86
DOI: 10.9734/jamcs/2021/v36i130332

In this paper, we show, by a new approach called SCD (Surjectivity by compactness and density), the internal exact controllability of the 1D heat equation by the use of strategic zone actuators. For the achievement of this objective, an operator (linear, continuous and surjective) built directly from the system allowed us to establish the exact result of controllability.

Open Access Original Research Article

On a Question of Prime Labeling of Graphs

A. M. C. U. M. Athapattu, P. G. R. S. Ranasinghe

Journal of Advances in Mathematics and Computer Science, Page 87-93
DOI: 10.9734/jamcs/2021/v36i130333

In the field of graph theory, the complete graph  of  vertices is a simple undirected graph such that every pair of distinct vertices is connected by a unique edge. In the present work, we introduce planar subgraph  of  with maximal number of edges . Generally,  does not admit prime labeling. We present an algorithm to obtain prime-labeled subgraphs of  . We conclude the paper by stating two conjectures based on labeling of . In particular, the planar subgraph admits anti-magic labeling but does not admit edge magic total labeling.

Open Access Original Research Article

Bayesian Estimation and Prediction for Exponentiated Generalized Inverted Kumaraswamy Distribution Based on Dual Generalized Order Statistics

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

Journal of Advances in Mathematics and Computer Science, Page 94-111
DOI: 10.9734/jamcs/2021/v36i130334

In this paper, the shape parameters, reliability and hazard rate functions of the exponentiated generalized inverted Kumaraswamy distribution are estimated using Bayesian approach. The Bayes estimators are derived under the squared error loss function and the linear-exponential loss function based on dual generalized order statistics. Credible intervals for the parameters, reliability and hazard rate functions are obtained. The Bayesian prediction (point and interval) for a future observation of the exponentiated generalized inverted Kumaraswamy distribution is obtained based on dual generalized order statistics. All results are specialized to lower record values and a numerical study is presented. Moreover, the theoretical results are applied on three real data sets.