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International Journal of Probability and Statistics
Number of Followers: 3  Open Access journalISSN (Print) 2168-4871 - ISSN (Online) 2168-4863 Published by SAP  [105 journals]
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- Estimation of Wind Power Using a New Two Variable Copula-based Model in
South Eastern Nigeria
Abstract: Publication year: 2022Source: International Journal of Probability and Statistics , Volume 11, Number 1Opabisi Adeyinka Kosemoni, Adeyemo Samuel O., Ohaegbulam Promise O.This study examines the use of other probability models as alternative for modeling wind speed data. The 2-parameter Weibull distribution is usually taken as the conventional model for fitting and analyzing wind speed observations. However, within the vanguard of statistical modeling, there exist other probability models which can also serve this purpose. In this paper, a study on ten probability models which can be used to fit wind speed observation is carried out. The models include: the Weibull, normal, Cauchy, gamma, power Lindley, generalized Lindley, generalized Rayleigh, generalized Maxwell, lognormal and the generalized exponential distributions. All ten models were used to fit monthly average wind speed observations from South-East Nigeria for the period (1987 – 2019). Results from the analysis showed that while the Weibull model remains a dominant model for the wind regime, the power Lindley and the normal distributions offered a very suitable alternative as well, as they offered very good fits to the wind speed observation which are indicative by their respective AIC, K-S and P-values.
- On Nonparametric Methods for Estimating the Hazard Function with
Application
Abstract: Publication year: 2022Source: International Journal of Probability and Statistics , Volume 11, Number 1Sahar Khairyfarag, Zohdy Mohamed Nofal, Mohamed Goda HindawyWhen a parametric form for the underlying distribution is not available, the estimation of hazard quantile is of major interest. Furthermore, the hazard quantile function can be employed instead of the hazard function. This work describes a new nonparametric hazard quantile function estimator based on TL-moments approaches in detail.
- Lebesgue−Chebyshev Synergism for the Bounds of Measurable Random
Variables
Abstract: Publication year: 2022Source: International Journal of Probability and Statistics , Volume 11, Number 1Francis Egenti Nzerem, Ukamaka Cynthia OrumieThe attainment of a near-faultless optimal estimate is always the chief goal in the application of measures. Boundedness is always an ‘essential commodity’ if optimality is desired. A function is Lebesgue integrable if theLebesgue integral does not ‘explode’; as well the existence of Chebyshev bound assures that the estimates of certain random variables or those of certain functionals, as the case may be, do not ‘explode’. The realization of the latter has the underpinning of Lebesgue measure applied on the set functions under consideration. Therefore, this work treated a veritable way of estimating the (maximal and minimal) bounds of Chebyshev-type inequalities, with the functions presupposed Lebesgue measurable.
- New Compounded Family of Distributions, with Applications
Abstract: Publication year: 2021Source: International Journal of Probability and Statistics , Volume 10, Number 3Abdul-Hadi N. Ahmed, Zohdy M. Nofal, Hager N. AhmedIn this thesis, We propose and study new compounding families, the truncated natural discrete Lindley with three distributions severally (Exponential distribution, Weibull distribution and Lomax distribution) this approach generates new distributions that extend well-known families of distributions. At the same time, they offer more flexibility for modeling lifetime data. The structural properties of the new distributions are investigated. These include the compounding representation of the distribution, reliability analysis and statistical measures. Expressions for Lorenz and Bonferroni curves and Renyi entropy as a measure for uncertainty reduction are derived.. The maximum likelihood method is used to estimate the model parameters. Two real-life data applications are proposed to illustrate the importance of the new families.
- Graphical Optimization of Mixture-Process Experiment: An Application to
Diabetes Mellitus Herbal Treatment
Abstract: Publication year: 2021Source: International Journal of Probability and Statistics , Volume 10, Number 3Gladys Gakenia NjorogeMany of the herbal medicines involving mixtures have process variables and assessing the effect of the mixture and process simultaneously is economical. Little application of designs of mixture-process experiments has been made on herbal medicine especially where optimization of both the mixture and process is concerned. This study set out to: carry out a mixture-process experiment using the most optimal split-plot design on herbal medicine for diabetes mellitus control using alloxan-induced diabetic albino wistar rats; and determine a model that provides a good fit to the experimental data and analyse it. To achieve the aims of the study, the most efficient optimal split-plot design was employed to obtain optimal mixture proportions of three herbal drugs and their extraction conditions on change of blood glucose level of alloxan-induced diabetic albino wistar rats. Secondly, a 28-term model was fitted to the experimental data, model adequacy tested and model reduction done accordingly. The final fitting model was used to carry out graphical optimization to obtain optimal mixture components and extraction conditions of the herbal formula. The general finding was that the single herbs were more effective than the complete mixtures with Cinnamomum verum being the most effective single herb. The extraction conditions of the herbs have an effect on the way the herbs, whether singly or in a mixture affect the response. Further, the optimal predicted response was 10.848mmol/l change in blood glucose level produced by a mixture blend of 491.5mg of Cinnamomum verum and 385.5mg of Gymnema sylvestre extracted at 25°C and a time of 15 minutes. These findings imply that mixing of herbs should only be done if it is experimentally proven that the mixture works better than the single herbs. The optimal extraction conditions for the herbs should be experimentally established for maximum effect. This further implies that any policies being formulated in order to regulate the standards and practise of herbal medicine should be based on research.
- A New Two-Parameter Compound G Family: Copulas, Properties and
Applications
Abstract: Publication year: 2021Source: International Journal of Probability and Statistics , Volume 10, Number 2Abdelrahman M. Khedr, Zohdy M. Nofal, Yehia M. El GebalyIn the work, we propose and study a new two-parameter compound G family of continuous distributions. Relevant statistical properties are mathematically derived. Many new G families of bivariate distributions are presented using Renyi's copula, Clayton copula, Ali-Mikhail-Haq copula, Farlie-Gumbel-Morgenstern copula, and modified Farlie-Gumbel-Morgenstern copula. Based on a special case we presented a new Lomax extension and studied its relevant statistical properties. The maximum likelihood method is used and employed for estimating the model parameters. Two application to real-life data sets are presented for illustrating the superiority of the new family.
- Berry-Esseen Type Bound in Partially Linear Regression Model under Mixing
Sequences
Abstract: Publication year: 2021Source: International Journal of Probability and Statistics , Volume 10, Number 2Sallieu Kabay SamuraIt is well-known that the confidence intervals of
and 
in partially linear regression model lie in the limit distributions of their estimators. However the accuracy of the confidence intervals depends on how fast the theoretical distributions of the estimators converge to their limits. As a results, Berry-Esseen type bounds can be used to assess the accuracy. The aim of this paper is to study the Barry-Esseen type bounds for the estimators of 
and 
in the partially linear regression model with 
satisfying 
with 
and 
being stationary 
-mixing random variables. By choosing suitable weighted functions, the Berry-Esseen type bounds for the estimators 
and 
can achieve 
and 
respectively. Simulation studies are conducted to demonstrate the performance of the proposed procedure.
- Interval Estimation for Burr Type-XII Model Based on the Generalized Order
Statistics
Abstract: Publication year: 2021Source: International Journal of Probability and Statistics , Volume 10, Number 1M. Maswadah, Seham M.In this paper, the conditional inference was applied to study some statistical properties for the confidence intervals of the Burr type-XII distribution parameters based on generalized order statistics. To measure the performance of this approach compared to the Asymptotic maximum likelihood estimates, simulation studies were performed for different values of sample sizes and shape parameters. The simulation results indicated that the conditional intervals possess good statistical properties and can perform well even when the sample size is small compared to the classical intervals. Finally, real data sets are given to illustrate the confidence intervals that were developed in this paper.
- Exponentiated Janardan Distribution: A Modification of Janardan
Distribution and Application to Life Time Data
Abstract: Publication year: 2021Source: International Journal of Probability and Statistics , Volume 10, Number 1Nelson Doe Dzivor, Henry Otoo, Eric Neebo WiahApplications of probability distributions have spread over the years from game of chance to all facet of life and disciplines. Due to quest of precision in modeling lifetime data, existing probability distributions are been improved upon through method of parameterization. This study introduced a new distribution called Exponentiated Janardan distribution of which Janardan distribution forms the baseline. This new distribution is a three-parameter distribution. Some statistical properties such as moments, MLE, survival/hazard rate are established. The proposed distribution was run on a number of life time datasets concurrently with the baseline distribution and the output result indicates that Exponentiated Janardan distribution produces smaller AIC value than the baseline distribution in all datasets considered. This indicates that Exponentiated Janardan distribution fits lifetime data more closely than Janardan distribution. The behavior of the pdf, survival function and hazard rate function are pictorially demonstrated. The role of each parameter in the proposed distribution is also pictorially demonstrated.
- On the Estimation of k-Regimes Switching of Mixture Autoregressive Model
via Weibull Distributional Random Noise
Abstract: Publication year: 2021Source: International Journal of Probability and Statistics , Volume 10, Number 1Rasaki Olawale Olanrewaju, Anthony Gichuhi Waititu, Nafiu Lukman AbiodunThis paper describes regime-switching, full range of shape changing distributions (multimodalities), and cycles traits that were characterized by time-varying series via Weibull distributional noise for time series with fluctuations and long-memory. We developed and established a Weibull Mixture Autoregressive model of k-regimes via
with Expectation-Maximization (EM) algorithm adopted as parameter estimation technique. The ergodic process for the 
model was ascertained via the maximized derivation of the absolute value of the subtraction of its likelihood from its expected likelihood.
