Pub Date : 2019-01-01DOI: 10.1080/25742558.2019.1660503
D. Satoh
Abstract A model selection method was proposed to determine the most appropriate model among growth curve models that have the same number of parameters. It uses a measure of mean relative squared error and regression equations from difference equations for growth curve models. The difference equations have exact solutions that are on exact solutions of differential equations as growth curve models. The regression equations from the difference equations perfectly reproduce their parameter estimates. The proposed method selects an appropriate model when data are on an exact solution of a differential equation. It was verified to be practical with six actual datasets when the Gompertz curve and logistic curve models, which are often used for forecasting, were alternative growth curve models.
{"title":"Model selection among growth curve models that have the same number of parameters","authors":"D. Satoh","doi":"10.1080/25742558.2019.1660503","DOIUrl":"https://doi.org/10.1080/25742558.2019.1660503","url":null,"abstract":"Abstract A model selection method was proposed to determine the most appropriate model among growth curve models that have the same number of parameters. It uses a measure of mean relative squared error and regression equations from difference equations for growth curve models. The difference equations have exact solutions that are on exact solutions of differential equations as growth curve models. The regression equations from the difference equations perfectly reproduce their parameter estimates. The proposed method selects an appropriate model when data are on an exact solution of a differential equation. It was verified to be practical with six actual datasets when the Gompertz curve and logistic curve models, which are often used for forecasting, were alternative growth curve models.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1660503","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42228491","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}
Pub Date : 2019-01-01DOI: 10.1080/25742558.2019.1622191
Kahkashan Ateeq, T. Qasim, Ayesha Rehman Alvi
Abstract In this article, we have derived a new distribution named as Rayleigh–Rayleigh distribution (RRD) motivated by the transformed transformer technique by Alzaatreh, Lee, and Famoye (2013). The statistical properties of RRD, comprising of explicit expressions for quantile function, moments, moment generating function, mean deviation, skewness, kurtosis, reliability measures, measures of uncertainty, distributions of order statistics and L moments have been derived. Parameter estimation is carried out using method of maximum-likelihood estimation and Fisher information matrix is derived. The flexibility of the new distribution is assessed by applying it to four real data sets. The comparative behavior of RRD with Rayleigh distribution, Generalized Rayleigh distribution, Exponentiated Rayleigh distribution, Weibull Rayleigh distribution and Alpha Power Rayleigh distribution provided the evidence that it outperforms the other competing distributions.
{"title":"An extension of Rayleigh distribution and applications","authors":"Kahkashan Ateeq, T. Qasim, Ayesha Rehman Alvi","doi":"10.1080/25742558.2019.1622191","DOIUrl":"https://doi.org/10.1080/25742558.2019.1622191","url":null,"abstract":"Abstract In this article, we have derived a new distribution named as Rayleigh–Rayleigh distribution (RRD) motivated by the transformed transformer technique by Alzaatreh, Lee, and Famoye (2013). The statistical properties of RRD, comprising of explicit expressions for quantile function, moments, moment generating function, mean deviation, skewness, kurtosis, reliability measures, measures of uncertainty, distributions of order statistics and L moments have been derived. Parameter estimation is carried out using method of maximum-likelihood estimation and Fisher information matrix is derived. The flexibility of the new distribution is assessed by applying it to four real data sets. The comparative behavior of RRD with Rayleigh distribution, Generalized Rayleigh distribution, Exponentiated Rayleigh distribution, Weibull Rayleigh distribution and Alpha Power Rayleigh distribution provided the evidence that it outperforms the other competing distributions.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1622191","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41374108","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}
Pub Date : 2019-01-01DOI: 10.1080/25742558.2019.1623647
J. Pandey, S. K. Upadhyay
Abstract The continuous wavelet transform of Schwartz tempered distributions is investigated and derive the corresponding wavelet inversion formula (valid modulo a constant-tempered distribution) interpreting convergence in . But uniqueness theorem for the present wavelet inversion formula is valid for the space obtained by filtering (deleting) (i) all non-zero constant distributions from the space , (ii) all non-zero constants that appear with a distribution as a union. As an example, in considering the distribution we would omit 1 and retain only . The wavelet kernel under consideration for determining the wavelet transform are those wavelets whose all the moments are non-zero. As an example, is such a wavelet. is an arbitrary constant. There exist many other classes of such wavelets. In our analysis, we do not use a wavelet kernel having any of its moments zero.
{"title":"Continuous wavelet transform of Schwartz tempered distributions","authors":"J. Pandey, S. K. Upadhyay","doi":"10.1080/25742558.2019.1623647","DOIUrl":"https://doi.org/10.1080/25742558.2019.1623647","url":null,"abstract":"Abstract The continuous wavelet transform of Schwartz tempered distributions is investigated and derive the corresponding wavelet inversion formula (valid modulo a constant-tempered distribution) interpreting convergence in . But uniqueness theorem for the present wavelet inversion formula is valid for the space obtained by filtering (deleting) (i) all non-zero constant distributions from the space , (ii) all non-zero constants that appear with a distribution as a union. As an example, in considering the distribution we would omit 1 and retain only . The wavelet kernel under consideration for determining the wavelet transform are those wavelets whose all the moments are non-zero. As an example, is such a wavelet. is an arbitrary constant. There exist many other classes of such wavelets. In our analysis, we do not use a wavelet kernel having any of its moments zero.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1623647","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42425411","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}
Pub Date : 2019-01-01DOI: 10.1080/25742558.2018.1564164
J. Ashraf, D. Balding
AbstractThe purpose of this paper is then to theoretically prove the estimated welfare measure from such elicitation method, which encompasses a complete decision process, is more efficient than th...
本文的目的是从理论上证明这种包含完整决策过程的启发式福利估计方法比其他方法更有效。。。
{"title":"RETRACTED ARTICLE: Design of an efficient and complete elicitation decision process in contingent valuation method","authors":"J. Ashraf, D. Balding","doi":"10.1080/25742558.2018.1564164","DOIUrl":"https://doi.org/10.1080/25742558.2018.1564164","url":null,"abstract":"AbstractThe purpose of this paper is then to theoretically prove the estimated welfare measure from such elicitation method, which encompasses a complete decision process, is more efficient than th...","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2018.1564164","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44133714","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}
Pub Date : 2019-01-01DOI: 10.1080/25742558.2019.1592276
Hojjatollah Amiri kayvanloo, M. Khanehgir, R. Allahyari
Abstract The aim of the present paper is to introduce a new family of measures of noncompactness on the Fréchet space LPloc(ℝN) (1 ≤ p < ∞). Further, we prove a fixed point theorem on the family of measures of noncompactness in LPloc(ℝN). As an application, we investigate the existence of entire solutions for some classes of nonlinear functional integral equations of convolution type associated with the new family of measures of noncompactness. Finally, we give an illustrative example to verify the effectiveness and applicability of our results.
{"title":"A family of measures of noncompactness in the space Lploc(ℝN) and its application to some nonlinear convolution type integral equations","authors":"Hojjatollah Amiri kayvanloo, M. Khanehgir, R. Allahyari","doi":"10.1080/25742558.2019.1592276","DOIUrl":"https://doi.org/10.1080/25742558.2019.1592276","url":null,"abstract":"Abstract The aim of the present paper is to introduce a new family of measures of noncompactness on the Fréchet space LPloc(ℝN) (1 ≤ p < ∞). Further, we prove a fixed point theorem on the family of measures of noncompactness in LPloc(ℝN). As an application, we investigate the existence of entire solutions for some classes of nonlinear functional integral equations of convolution type associated with the new family of measures of noncompactness. Finally, we give an illustrative example to verify the effectiveness and applicability of our results.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1592276","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46559195","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}
Pub Date : 2019-01-01DOI: 10.1080/25742558.2019.1568662
P. E. Oguntunde, M. A. Khaleel, Mohammed T. Ahmed, H. Okagbue
Abstract In this paper, a new compound continuous distribution named the Gompertz Fréchet distribution which extends the Frèchet distribution was developed. Its various statistical properties were also derived and estimation of model parameters was considered using the maximum likelihood estimation method. The application of the Gompertz Fréchet distribution was provided using real-life data sets and its performance was compared with Gompertz Weibull distribution, Gompertz Lomax distribution and Gompertz Burr XII distribution.
{"title":"The Gompertz Fréchet distribution: Properties and applications","authors":"P. E. Oguntunde, M. A. Khaleel, Mohammed T. Ahmed, H. Okagbue","doi":"10.1080/25742558.2019.1568662","DOIUrl":"https://doi.org/10.1080/25742558.2019.1568662","url":null,"abstract":"Abstract In this paper, a new compound continuous distribution named the Gompertz Fréchet distribution which extends the Frèchet distribution was developed. Its various statistical properties were also derived and estimation of model parameters was considered using the maximum likelihood estimation method. The application of the Gompertz Fréchet distribution was provided using real-life data sets and its performance was compared with Gompertz Weibull distribution, Gompertz Lomax distribution and Gompertz Burr XII distribution.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1568662","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45768019","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}
Pub Date : 2019-01-01DOI: 10.1080/25742558.2019.1602929
Dilanka S. Dedduwakumara, L. Prendergast, R. Staudte
Abstract The four-parameter Generalized Lambda distribution (GLD) can be used to approximate many probability distributions. We present a simple and efficient two-stage process for finding optimal GLD parameters to approximate a specified distribution. The probability density quantile function is first used to find the best GLD shape parameters. Given those shape parameters, it is then straightforward to find the best location and scale parameters. We highlight the excellent performance of our approach with comparisons to two existing and popular methods for a wide choice of distributions. Finally, we show that this is method can be used with other distributions by providing applications also to the Generalized Beta distribution.
{"title":"A simple and efficient method for finding the closest generalized lambda distribution to a specific model","authors":"Dilanka S. Dedduwakumara, L. Prendergast, R. Staudte","doi":"10.1080/25742558.2019.1602929","DOIUrl":"https://doi.org/10.1080/25742558.2019.1602929","url":null,"abstract":"Abstract The four-parameter Generalized Lambda distribution (GLD) can be used to approximate many probability distributions. We present a simple and efficient two-stage process for finding optimal GLD parameters to approximate a specified distribution. The probability density quantile function is first used to find the best GLD shape parameters. Given those shape parameters, it is then straightforward to find the best location and scale parameters. We highlight the excellent performance of our approach with comparisons to two existing and popular methods for a wide choice of distributions. Finally, we show that this is method can be used with other distributions by providing applications also to the Generalized Beta distribution.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1602929","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45955825","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}
Pub Date : 2019-01-01DOI: 10.1080/25742558.2019.1634316
Y. Mehraliyev, B. Valiyeva, A. Ramazanova
Abstract The work is devoted to the study of the solvability of an inverse boundary value problem with an unknown time-dependent coefficient for the linearized Benney–Luke equation with non-conjugate boundary conditions and integral conditions. The goal of the paper consists of the determination of the unknown coefficient together with the solution. The problem is considered in a rectangular domain. The definition of the classical solution of the problem is given. First, the given problem is reduced to an equivalent problem in a certain sense. Then, using the Fourier method the equivalent problem is reduced to solving the system of integral equations. Thus, the solution of an auxiliary inverse boundary value problem reduces to a system of three nonlinear integro-differential equations for unknown functions. Concrete Banach space is constructed. Further, in the ball from the constructed Banach space by the contraction mapping principle, the solvability of the system of nonlinear integro-differential equations is proved. This solution is also a unique solution to the equivalent problem. Finally, by equivalence, the theorem of existence and uniqueness of a classical solution to the given problem is proved.
{"title":"An inverse boundary value problem for a linearized Benny–Luc equation with nonlocal boundary conditions","authors":"Y. Mehraliyev, B. Valiyeva, A. Ramazanova","doi":"10.1080/25742558.2019.1634316","DOIUrl":"https://doi.org/10.1080/25742558.2019.1634316","url":null,"abstract":"Abstract The work is devoted to the study of the solvability of an inverse boundary value problem with an unknown time-dependent coefficient for the linearized Benney–Luke equation with non-conjugate boundary conditions and integral conditions. The goal of the paper consists of the determination of the unknown coefficient together with the solution. The problem is considered in a rectangular domain. The definition of the classical solution of the problem is given. First, the given problem is reduced to an equivalent problem in a certain sense. Then, using the Fourier method the equivalent problem is reduced to solving the system of integral equations. Thus, the solution of an auxiliary inverse boundary value problem reduces to a system of three nonlinear integro-differential equations for unknown functions. Concrete Banach space is constructed. Further, in the ball from the constructed Banach space by the contraction mapping principle, the solvability of the system of nonlinear integro-differential equations is proved. This solution is also a unique solution to the equivalent problem. Finally, by equivalence, the theorem of existence and uniqueness of a classical solution to the given problem is proved.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1634316","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48683251","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}
Pub Date : 2019-01-01DOI: 10.1080/25742558.2019.1701377
D. Kareithi, D. Salifu, N. Owuor, S. Subramanian, E. Tonnang, Yuriy Rogovchenko
Abstract Data collection in life table experiments is generally time-consuming and costly such that data reconstruction of published information provides an avenue to access the original data for purposes of further investigation. In this paper, we present an algorithm that reconstructs life table raw data using a summary of results from published articles. We present the steps of the development and implementation (in the R computer language) of the algorithm, its scope of application, assumptions, and limitations. Statistical background of the algorithm is also presented. The developed algorithm was then applied to reconstruction of life table data of two insect species, Chilo partellus and Busseola fusca, from published information. Welch’s two-sample t-test was applied to test the difference between the original and reconstructed data of the insect life stages. C. Partellus results were not significantly different, but, for B. fusca, pupa development time, and larva and pupa development rate were significantly different at the 95% confidence level. It is concluded that the algorithm could be used to reconstruct original data sets from cohort life table data sets of insects, given published information and sample sizes.
{"title":"An algorithm for data reconstruction from published articles – Application on insect life tables","authors":"D. Kareithi, D. Salifu, N. Owuor, S. Subramanian, E. Tonnang, Yuriy Rogovchenko","doi":"10.1080/25742558.2019.1701377","DOIUrl":"https://doi.org/10.1080/25742558.2019.1701377","url":null,"abstract":"Abstract Data collection in life table experiments is generally time-consuming and costly such that data reconstruction of published information provides an avenue to access the original data for purposes of further investigation. In this paper, we present an algorithm that reconstructs life table raw data using a summary of results from published articles. We present the steps of the development and implementation (in the R computer language) of the algorithm, its scope of application, assumptions, and limitations. Statistical background of the algorithm is also presented. The developed algorithm was then applied to reconstruction of life table data of two insect species, Chilo partellus and Busseola fusca, from published information. Welch’s two-sample t-test was applied to test the difference between the original and reconstructed data of the insect life stages. C. Partellus results were not significantly different, but, for B. fusca, pupa development time, and larva and pupa development rate were significantly different at the 95% confidence level. It is concluded that the algorithm could be used to reconstruct original data sets from cohort life table data sets of insects, given published information and sample sizes.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1701377","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47668386","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}
Pub Date : 2019-01-01DOI: 10.1080/25742558.2019.1655870
K. Eke, V. Olisama, S. Bishop
Abstract In this research work, convexity condition is introduced to some classes of contraction mappings such as Chatterjea and Hardy and Rogers contractive mappings. The fixed points of these maps are proved in complete metric spaces. Example is equally provided to support the main result. The unique solution of nonlinear Fredholm integral equation is obtained via the Hardy and Rogers convex contraction mappings of type 2. The results obtained in this paper, extend and generalize some related works in the literature.
{"title":"Some fixed point theorems for convex contractive mappings in complete metric spaces with applications","authors":"K. Eke, V. Olisama, S. Bishop","doi":"10.1080/25742558.2019.1655870","DOIUrl":"https://doi.org/10.1080/25742558.2019.1655870","url":null,"abstract":"Abstract In this research work, convexity condition is introduced to some classes of contraction mappings such as Chatterjea and Hardy and Rogers contractive mappings. The fixed points of these maps are proved in complete metric spaces. Example is equally provided to support the main result. The unique solution of nonlinear Fredholm integral equation is obtained via the Hardy and Rogers convex contraction mappings of type 2. The results obtained in this paper, extend and generalize some related works in the literature.","PeriodicalId":92618,"journal":{"name":"Cogent mathematics & statistics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/25742558.2019.1655870","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45226846","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}
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