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International Journal of Probability and Statistics
Number of Followers: 3

This is an Open Access Journal

Open Access journal
ISSN (Print) 2168-4871 - ISSN (Online) 2168-4863
Published by SAP

[105 journals]

Managing Risk of Spreading "COVID-19" in Egypt: Modelling Using a Discrete
Marshall–Olkin Generalized Exponential Distribution
- Abstract: Publication year: 2020Source: International Journal of Probability and Statistics , Volume 9, Number 2Ehab M. Almetwally, Hisham M. Almongy, Hany A. SalehThis research aims at modeling the risks of COVID-19 spread in Egypt, by specifying an optimal statistical model to analyse the daily count of COVID-19 new cases. A new three-parameter discrete distributions has been developed namely, the Discrete Marshall–Olkin Generalized Exponential (DMOGEx) distribution. Probability mass function, hazard rate and some statistical properties of reliability are discussed. Parameter estimation of the Based on the maximum likelihood estimation (MLE) method is discussed for the DMOGEx distribution. Numerical study was done using daily count of new cases in Egypt, empirical results were interpreted in detail and expectation probabilities for daily new cases were discussed. Monte Carlo Simulation has been performed to evaluate the restricted sample properties of the proposed distribution.
A New Two-Parameter Poisson-Sujatha Distribution
- Abstract: Publication year: 2020Source: International Journal of Probability and Statistics , Volume 9, Number 2Rama Shanker, Kamlesh Kumar Shukla, Tekie Asehun LeonidaA new two-parameter Poisson-Sujatha distribution, a Poisson mixture of a new two-parameter Sujatha distribution, which includes Poisson-Sujatha distribution and Poisson-Akash distribution as particular cases, has been introduced. Its moments based statistical measures including coefficient of variation, skewness, kurtosis and index of dispersion have been obtained. Maximum likelihood estimation has been explained for estimating its parameters. Goodness of fit of the proposed distribution has been explained with six over-dispersed count datasets and fit has been compared with Poisson-Sujatha distribution and other generalizations of Poisson-Sujatha distributions
Structural Models for Analyzing Survival Data with Multiple Time-dependent
Treatments
- Abstract: Publication year: 2020Source: International Journal of Probability and Statistics , Volume 9, Number 1Yeqian Liu, Yingxiao HuangIn randomized clinical trials involving survival time, patients may initiate secondary salvage treatments during the follow-up in order to prolong survival. As a result, the effect of primary treatment is usually confounded by these secondary treatments. In addition, such secondary salvage treatments are usually time-dependent due to being initiated upon adverse reaction, disease progression, etc. In this paper, we adopt two types of structural models: structural nested models and marginal structural Cox models, and propose an inferential procedure that improves the efficiency of the usual IPTW method. We examine the finite-sample performance of the proposed method by simulation studies and by application to data from a cancer clinical trial.
The Zero Inflated Negative Binomial - Shanker Distribution and Its
Application to HIV Exposed Infant Data
- Abstract: Publication year: 2020Source: International Journal of Probability and Statistics , Volume 9, Number 1Stella Kibika, Collins Odhiambo, Elphas OkangoMotivated by HIV exposed infants (HEI) sero-conversion data, we provide an extension of Zero-inflated Negative Binomial (ZINB) distribution to Zero Inflated Negative Binomial - Shanker (ZINB-SH) distribution. In this setting the ZINB-SH, distribution provides an alternative to the Poisson-Shanker distribution in particular, when data exhibits over dispersion brought by excess zeros. The HIV Exposed infant data is characterized by both structured and non-structured zeroes which makes the feature ideal in this context. We describe the properties of ZINB-SH distribution and estimate its parameters. Extensive simulations were conducted and the results in terms of goodness-of-fit, compared to the standard Negative Binomial, Shanker, Zero-Inflated Negative Binomial and Negative Binomial –Shanker distributions. The ZINB-SH distribution is competitive under different settings of simulation and does well as sample size increases. To validate the distribution, we apply real typical HIV-Infant exposed data.
The Analysis of Mixed Model in Time Series Decomposition
- Abstract: Publication year: 2020Source: International Journal of Probability and Statistics , Volume 9, Number 1Kelechukwu C. N. Dozie, Hope I. Mbachu, Mirian C. RaymondThis paper examines the condition(s) under which the mixed model is the most appropriate model in descriptive time series analysis when trend-cycle component is linear. Since some existing studies have adequately characterized the additive model, the analyst is still exposed to the risk of wrongly using multiplicative model when mixed model should be used. Therefore, the aim of this study is to identify the series that admits mixed model. The method employed in this paper is the Buys-Ballot procedure developed for choice of model and choice of appropriate transformations, among other uses, based on row, column and over totals, means and variances of the Buys-Ballot table. Results show that, 1) the seasonal variance of the Buys-Ballot table, for the mixed model, a function of the slope and seasonal effect only. 2) the calculated values of the test statistic identified the mixed model correctly in 99 out the 100 stimulations.
Exchange Rate Forecasting Using Non-linear Threshold Models
- Abstract: Publication year: 2019Source: International Journal of Probability and Statistics , Volume 8, Number 2Akintunde Mutairu Oyewale, Chigozie Kelechi Acha, Agunloye Oluokun Kasali, Eriobu Nkiru Obioma, Oyekunle Janet Olufunmike, Abdulazeez Ismail AdeyinkaForeign exchange is one of the most important financial instruments very volatile and chaotic in nature. Nowadays, the role of the foreign exchange market is becoming more and more important in the financial markets around the world; it remains the only instruments worldwide to measure the standard of living, Economic performance and country standing among the committee of nations. The foreign exchange market which is an over-the-counter market is used for the trading of currencies. It makes the foreign exchange market the largest and most liquid market among the financial markets. Necessary mathematical frame work was put in place, this was illustrated with data from record of Central Bank of Nigeria through their official website. Through this the performance of nonlinear threshold models in forecasting the exchange rate of Nigeria in relation to United States of American dollar as bench mark. The software used for the analysis was Econometrics View (E-view). Stationarity tests were carried out before the analysis, (the original data was not stationary, but at first difference it was stationary, thereafter comprehensive data analysis was performed). The forecasting results indicate that SETAR models did not outperform Random Walk in any period. TAR models offered promising results in the period. This study supports the general belief that the exchange rates are chaotic, volatile and very difficult to forecast and this applies to Exchange rate system of Nigeria as it is the case in the developed world.
Parity Progression Estimation and Categorical Analysis of Birth Cohort
Data in Ghana: The Case of Birth Data Derived from Health Insurance Data
- Abstract: Publication year: 2019Source: International Journal of Probability and Statistics , Volume 8, Number 2Bosson-Amedenu Senyefia, Habib Bipembi, Toffe GladysThis paper sought to estimate the effect of socioeconomic variables such as education level, type of employment and settlement type on the fertility rate of women in Ghana using the method of cohort Total fertility rate (TFRc) computed through parity progression ratios (PPRs) and the use of survival and categorical analyses to determine the relationship among the categories. The Kaplan Meier statistics showed a significant difference among the six categories. The hazard function plot showed that the women who have low education and women in informal employment have the highest hazard in terms of fertility (they tend to have more children than the other treatment categories) followed by women in rural settlement. However, the survival plot shows that women with high education level and those in formal employment have performed better (they tend to have fewer children) followed by women living in sub-urban settlement. Formal workers were found to have lower fertility rate compared to informal workers (TFRc: 2.1
Effects of Influential Outliers in Local Polynomial Techniques (Smoothing
Techniques)
- Abstract: Publication year: 2019Source: International Journal of Probability and Statistics , Volume 8, Number 1Edith U. Umeh, Chinyere I. OjukwuThis paper which discusses effects of influential outliers in local polynomial techniques (Kernel and Spline) aimed at determining the robust outliers where more than two independent variables are included in the model and to determine the best type of technique to be used for outlier treatment and its influence on the model performance. During the analysis, kernel and spline methods were applied on the Gross Domestic Product (GDP) of Nigeria, for the period of twelve years (1981 to 2012) from National Bureau of Statistics (NBS) using SPSS and Minitab to check whether outliers can be smoothed out during smoothing which was proved otherwise. Thus, three methods of outlier detection and elimination in local polynomial techniques namely Leverages, Mahalanobis distance and DFFITS were used to detect the influential outliers before smoothing. Seven outliers were detected from Mahalanobis distance with five high leverage cases and three influential outliers from DFFITS method. This inferential outliers affect the regression equation thereby deteriorate the model performance. It is therefore recommended that researchers carrying out research on smoothing techniques should detect and eliminate influential outliers before smoothing; hence the relevance of the effect of influential outliers in local polynomial techniques cannot be undermined.
Ordered Logistic Regression on the Mental Health of Undergraduate Students
- Abstract: Publication year: 2019Source: International Journal of Probability and Statistics , Volume 8, Number 1Maureen T. Nwakuya, Omosivie MmadukaMental health is the state of well-being of an individual, were such individual can cope with the stresses of life and still make contribution to his/her community. Research has shown that there is an association between behavioral tendencies of undergraduate students and their mental health. This we believe is due to stress of full time academic program. Bearing this in mind we focused our research in identifying these factors that affect the mental health of students and ascertain the level of relationship between them and the student’s mental health. We adopted the stratified sampling technique for data collection and used self-administered questionnaire to identify the prevalence of factors known to be associated with mental health. The ordered logistic regression was carried out to obtain a proportional odds model that was used to model this relationship. The results show that when the current well-being of the students increase by a unit the odds of mental health state of the student being in an unstable state or mildly-unstable state versus stable state increases by 36.27%, given that any other variable is held constant. Also when the coping strategy increases the odds also increases by 33.16%, we can also observe that increase in the mental health assessment also increases the odds of mental health in unstable or mildly unstable state versus stable state, by 22.49%. A close look at the odds ratio and the regression coefficients makes us conclude that the most influential factors of the mental health is the current well-being of the student, followed by coping strategies and lastly the mental health assessment.
A Generalization of Two-Parameter Lindley Distribution with Properties and
Applications
- Abstract: Publication year: 2019Source: International Journal of Probability and Statistics , Volume 8, Number 1Rama Shanker, Kamlesh Kumar Shukla, Tekie Asehun LeonidaIn this paper, a generalization of two-parameter Lindley distribution (GTPLD), which includes one parameter exponential and Lindley distributions, two-parameter Lindley distribution (TPLD) of Shanker and Mishra (2013), Weibull distribution, gamma distribution, generalized gamma distribution of Stacy (1962) and power Lindley distribution of Ghitany et al (2013) as particular cases, has been proposed. Its moments, hazard rate function, mean residual life function, order statistic, Renyi entropy measure has been studied. Method of maximum likelihood estimation has been discussed for estimating its parameters. Applications of the distribution have been explained with two examples of observed real lifetime datasets.