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Exponentiated Half Logistic-Generalized G Power Series Class of Distributions: Properties and Applications 幂次半logistic -广义G幂级数类分布:性质及应用
Journal of Probability and Statistical Science Pub Date : 2022-10-03 DOI: 10.37119/jpss2022.v20i1.514
Simbarashe Chamunorwa, B. Oluyede, Fastel Chipepa, B. Makubate, Chipo Zidana
{"title":"Exponentiated Half Logistic-Generalized G Power Series Class of Distributions: Properties and Applications","authors":"Simbarashe Chamunorwa, B. Oluyede, Fastel Chipepa, B. Makubate, Chipo Zidana","doi":"10.37119/jpss2022.v20i1.514","DOIUrl":"https://doi.org/10.37119/jpss2022.v20i1.514","url":null,"abstract":"A new generalized class of distributions called the Exponentiated Half Logistic-Generalized G Power Series (EHL-GGPS) distribution is proposed. We present some special cases in the proposed distribution. Several mathematical properties of the EHL-GGPS distribution were also derived including order statistics, moments and maximum likelihood estimates. A simulation study for selected parameter values is presented to examine the consistency of the maximum likelihood estimates. Finally, some real data applications of the EHL-GGPS distribution are presented to illustrate the usefulness of the proposed class of distributions.","PeriodicalId":161562,"journal":{"name":"Journal of Probability and Statistical Science","volume":"48 6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133899283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
New defective models based on the Topp-Leone generated family of distributions 基于Topp-Leone生成的分布族的新缺陷模型
Journal of Probability and Statistical Science Pub Date : 2022-10-03 DOI: 10.37119/jpss2022.v20i1.521
Weizhong Tian, Tingting Liu, Yaoting Yang, Arjun K. Gupta
{"title":"New defective models based on the Topp-Leone generated family of distributions","authors":"Weizhong Tian, Tingting Liu, Yaoting Yang, Arjun K. Gupta","doi":"10.37119/jpss2022.v20i1.521","DOIUrl":"https://doi.org/10.37119/jpss2022.v20i1.521","url":null,"abstract":"This paper proposes two new defective models based on the Topp-Leone (TL) gen-erated family of distributions. Unlike most of the cure rate models, the advantage of the defective model is that the cure rate can be modeled without adding any addi-tional parameters to the model. The maximum likelihood function (MLE) is discussed for these models, and the asymptotic property of MLE is verified by simulation. The applications of this method are illustrated by three real data sets.","PeriodicalId":161562,"journal":{"name":"Journal of Probability and Statistical Science","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130518391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Marshall-Olkin-Type II-Topp-Leone-G Family of Distributions: Model, Properties and Applications Marshall-Olkin-Type II-Topp-Leone-G族分布:模型、性质及应用
Journal of Probability and Statistical Science Pub Date : 2022-10-03 DOI: 10.37119/jpss2022.v20i1.508
Kethamile Rannona, B. Oluyede, Fastel Chipepa, B. Makubate
{"title":"Marshall-Olkin-Type II-Topp-Leone-G Family of Distributions: Model, Properties and Applications","authors":"Kethamile Rannona, B. Oluyede, Fastel Chipepa, B. Makubate","doi":"10.37119/jpss2022.v20i1.508","DOIUrl":"https://doi.org/10.37119/jpss2022.v20i1.508","url":null,"abstract":"We develop a new family of distribution called the Marshall-Olkin-Type II-Topp-Leone-G (MO-TII-TL-G) family of distributions, which is a linear combination of the exponential-G family of distributions. The statistical properties of the new distributions are studied and its model parameters are obtainedusing the maximum likelihood method. A simulation study is carried out to determine the performance of the maximum likelihood estimates and lastly real data examples are provided to demonstrate the usefulness of the proposed model in comparison to other models.","PeriodicalId":161562,"journal":{"name":"Journal of Probability and Statistical Science","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123276910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Exceedance probability analysis: a practical and effective alternative to t-tests 超越概率分析:一种替代t检验的实用而有效的方法
Journal of Probability and Statistical Science Pub Date : 2022-10-03 DOI: 10.37119/jpss2022.v20i1.513
Hening Huang
{"title":"Exceedance probability analysis: a practical and effective alternative to t-tests","authors":"Hening Huang","doi":"10.37119/jpss2022.v20i1.513","DOIUrl":"https://doi.org/10.37119/jpss2022.v20i1.513","url":null,"abstract":"This paper presents a practical and effective alternative to the traditional t-tests for (1) comparing a sample or sample mean against a known mean (i.e. one-sample test) and (2) comparing two samples or two sample means (i.e. two-sample test).  The proposed method is referred to as exceedance probability (EP) analysis.  In a one-sample test, EP is defined as the probability that a sample or sample mean is greater than a known mean.   In a two-sample test, EP is defined as the probability that the difference between two samples or between two sample means is greater than a specified value (referred to as probabilistic effect size (PES)).  This paper also defines a new statistic called relative mean effect size (RMES).  RMES provides a true measure of the scientific significance (not the statistical significance) of the difference between two means.  A case study of preference between two manufacturers is presented to demonstrate the effectiveness of the proposed EP analysis, compared with four existing methods: t-tests, common language effect size (CL) analysis, signal content index (SCI) analysis, and Bayesian analysis.  Unlike these existing methods that require the assumption of normality, the proposed EP analysis can be performed with any type of distributions.  The case study example is examined with a normal distribution model and a raised cosine distribution model.  The former is solved with an analytical solution and the latter is solved with a numerical method known as probability domain simulation (PDS).","PeriodicalId":161562,"journal":{"name":"Journal of Probability and Statistical Science","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134495243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Deriving the Least Squares Estimates in Introductory Regression Courses 关于回归入门课程中最小二乘估计的推导
Journal of Probability and Statistical Science Pub Date : 2022-10-03 DOI: 10.37119/jpss2022.v20i1.506
M. Inlow
{"title":"On Deriving the Least Squares Estimates in Introductory Regression Courses","authors":"M. Inlow","doi":"10.37119/jpss2022.v20i1.506","DOIUrl":"https://doi.org/10.37119/jpss2022.v20i1.506","url":null,"abstract":"Introductory regression books typically begin their derivation of the least squares matrix estimation formula by considering the simple linear regression model. We suggest beginning with the zero-intercept model which has advantages. We provide two examples of this approach, one of which is a new, non-calculus derivation using the Cauchy-Schwarz inequality. \u0000 ","PeriodicalId":161562,"journal":{"name":"Journal of Probability and Statistical Science","volume":"115 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123467470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Gompertz-Topp Leone-G Family of Distributions with Applications Gompertz-Topp Leone-G族分布及其应用
Journal of Probability and Statistical Science Pub Date : 2022-10-03 DOI: 10.37119/jpss2022.v20i1.630
Kethamile Rannona, B. Oluyede, Simbarashe Chamunorwa
{"title":"The Gompertz-Topp Leone-G Family of Distributions with Applications","authors":"Kethamile Rannona, B. Oluyede, Simbarashe Chamunorwa","doi":"10.37119/jpss2022.v20i1.630","DOIUrl":"https://doi.org/10.37119/jpss2022.v20i1.630","url":null,"abstract":"We introduce a new family of distributions, referred to as the Gompertz-Topp-Leone-G (Gom-TL-G) distribution. The new family of distributions can be expressed as an infinite linear combination of the Exp-G distributions. It can handle extremely tailed data and has both monotonic and non-monotonic hazard rate functions. A simulation study is used to assess the estimation method. Some real data examples are analyzed for illustrative purposes.","PeriodicalId":161562,"journal":{"name":"Journal of Probability and Statistical Science","volume":"111 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131272943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Marshall-Olkin-Odd Power Generalized Weibull-G Family of Distributions with Applications of COVID-19 Data 基于COVID-19数据应用的Marshall-Olkin-Odd幂广义Weibull-G族分布
Journal of Probability and Statistical Science Pub Date : 2022-10-03 DOI: 10.37119/jpss2022.v20i1.509
Fastel Chipepa, Thatayaone Moakofi, B. Oluyede
{"title":"Marshall-Olkin-Odd Power Generalized Weibull-G Family of Distributions with Applications of COVID-19 Data","authors":"Fastel Chipepa, Thatayaone Moakofi, B. Oluyede","doi":"10.37119/jpss2022.v20i1.509","DOIUrl":"https://doi.org/10.37119/jpss2022.v20i1.509","url":null,"abstract":"Attempts have been made to define new families of distributions that provide more flexibility for modelling data that is skewed in nature. In this work, we propose a new family of distributions called  Marshall-Olkin-odd power generalized Weibull (MO-OPGW-G) distribution based on the generator pioneered by Marshall and Olkin [20]. This new family of distributions allows for a flexible fit to real data from several fields, such as engineering, hydrology and survival analysis. The mathematical and statistical properties of these distributions are studied and its model parameters are obtained through the maximum likelihood method. We finally demonstrate the effectiveness of these models via simulation experiments and applications to COVID-19 daily deaths data sets.","PeriodicalId":161562,"journal":{"name":"Journal of Probability and Statistical Science","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124959360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Estimating the Parameters of a Simple Linear Regression Model Without Using Differential Calculus 不使用微分法估计简单线性回归模型的参数
Journal of Probability and Statistical Science Pub Date : 2022-10-03 DOI: 10.37119/jpss2022.v20i1.645
J. Sarkar, Mamunur Rashid
{"title":"Estimating the Parameters of a Simple Linear Regression Model Without Using Differential Calculus","authors":"J. Sarkar, Mamunur Rashid","doi":"10.37119/jpss2022.v20i1.645","DOIUrl":"https://doi.org/10.37119/jpss2022.v20i1.645","url":null,"abstract":"To estimate the parameters of a simple linear regression model, students who already know calculus can minimize the total squared deviations by setting its first-order partial derivatives to zero and solving simultaneously. For students who do not know calculus, most teachers/textbooks simply state the formulas without justifying them. Students accept the formulas on faith; and for given data, they evaluate the estimates using a calculator or a statistical software. In this paper, we justify the formulas without invoking calculus. We hope the users of statistics will benefit from our proposed justifications.","PeriodicalId":161562,"journal":{"name":"Journal of Probability and Statistical Science","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128265361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic Properties of MLE's for Distributions Generated from an Exponential Distribution by a Generalized Log-Logistic Transformation 用广义对数-逻辑变换从指数分布生成的分布的最大似然渐近性质
Journal of Probability and Statistical Science Pub Date : 2022-10-03 DOI: 10.37119/jpss2022.v20i1.543
J. Gleaton, Ping Sa, S. Hamid
{"title":"Asymptotic Properties of MLE's for Distributions Generated from an Exponential Distribution by a Generalized Log-Logistic Transformation","authors":"J. Gleaton, Ping Sa, S. Hamid","doi":"10.37119/jpss2022.v20i1.543","DOIUrl":"https://doi.org/10.37119/jpss2022.v20i1.543","url":null,"abstract":"ABSTRACT.  A generalized log-logistic (GLL) family of lifetime distributions is one in which any pair of distributions are related through a GLL transformation, for some (non-negative) value of the transformation parameter k (the odds function of the second distribution is the k-th power of the odds function of the first distribution).  We consider GLL families generated from an exponential distribution.  It is shown that the Maximum Likelihood Estimators (MLE’s) for the parameters of the generated, or composite, distribution have the properties of strong consistency and asymptotic normality and efficiency.  Data simulation is also found to support the condition of asymptotic efficiency.    \u0000  \u0000Keywords Generalized log-logistic exponential distribution; asymptotic properties of MLE’s; simulation","PeriodicalId":161562,"journal":{"name":"Journal of Probability and Statistical Science","volume":"85 16","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133748770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Forecasting of Immigrants in Canada using Forecasting models 用预测模型预测加拿大移民
Journal of Probability and Statistical Science Pub Date : 2022-10-03 DOI: 10.37119/jpss2022.v20i1.511
S. Pandher, Arzu Sardarli, Andrei Volodin
{"title":"Forecasting of Immigrants in Canada using Forecasting models","authors":"S. Pandher, Arzu Sardarli, Andrei Volodin","doi":"10.37119/jpss2022.v20i1.511","DOIUrl":"https://doi.org/10.37119/jpss2022.v20i1.511","url":null,"abstract":"In Canada, the number of international students, temporary workers and refugees from every part of the world grows each year. Therefore, forecasting immigration is important for the economy of Canada and Labor Market. In this regard, four forecasting approaches have been applied to the annual data of immigrants for the period 2000-2019. The accuracy of Moving average (MA), Autoregressive (AR), Autoregressive moving average (ARMA), Autoregressive integrated moving average (ARIMA) models were checked via comparing Akaike’s information criteria(AIC), Bayesian information criteria (BIC), Mean error (ME), Root mean square error(RMSE), Mean absolute error (MAE), Mean percentage error (MPE), Mean absolute percentage error (MAPE) and Mean absolute scaled error (MASE) and graphical approaches such as ACF plots of residuals. Experimental results showed that ARIMA (1,2,4) is the best-fitted model for forecasting immigrants in Canada. Selected forecasting approaches are applied to predict immigrants for five years from 2020-2024.","PeriodicalId":161562,"journal":{"name":"Journal of Probability and Statistical Science","volume":"142 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131635429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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