This paper proposes a new probability distribution called as type II truncated Fréchet inverse exponential distribution. Fundamental statistical properties like moments, incomplete moments, and quantile function of the proposed model are studied. The estimation of the parameter of the new model is approached by maximum likelihood method based on complete and censored samples. Asymptotic confidence interval of model parameters is investigated. We assess the numerical results to study the theoretical results. Superiority of the type II truncated Fréchet inverse exponential model over some known distributions is showed through one real data set.
{"title":"Estimation of type II truncated Fr'echet inverse exponential distribution under censored data","authors":"Maha A. Aldahlan","doi":"10.22436/jnsa.013.06.05","DOIUrl":"https://doi.org/10.22436/jnsa.013.06.05","url":null,"abstract":"This paper proposes a new probability distribution called as type II truncated Fréchet inverse exponential distribution. Fundamental statistical properties like moments, incomplete moments, and quantile function of the proposed model are studied. The estimation of the parameter of the new model is approached by maximum likelihood method based on complete and censored samples. Asymptotic confidence interval of model parameters is investigated. We assess the numerical results to study the theoretical results. Superiority of the type II truncated Fréchet inverse exponential model over some known distributions is showed through one real data set.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"51 1","pages":"354-363"},"PeriodicalIF":0.0,"publicationDate":"2020-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75435199","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}
In this paper, we introduce a new extension of the Inverse Weibull distribution along with a number of its mathematical properties. Next, we construct a modified Chi-squared goodness-of-fit test based on the Nikulin-Rao-Robson statistic for censored and complete data. We describe the theory and the mechanism of the Y2 n test statistic which can be used in survival and reliability data analysis. We use the maximum likelihood estimators based on the initial non grouped data sets. Then, we conduct numerical simulations to reinforce the results. For showing the applicability of our model in various fields, we illustrate the proposed test by applications to two real data sets for complete data case and two other data sets in the presence of right censored.
{"title":"Lomax inverse Weibull model: properties, applications, and a modified Chi-squared goodness-of-fit test for validation","authors":"H. Goual, H. Yousof, M. M. Ali","doi":"10.22436/jnsa.013.06.04","DOIUrl":"https://doi.org/10.22436/jnsa.013.06.04","url":null,"abstract":"In this paper, we introduce a new extension of the Inverse Weibull distribution along with a number of its mathematical properties. Next, we construct a modified Chi-squared goodness-of-fit test based on the Nikulin-Rao-Robson statistic for censored and complete data. We describe the theory and the mechanism of the Y2 n test statistic which can be used in survival and reliability data analysis. We use the maximum likelihood estimators based on the initial non grouped data sets. Then, we conduct numerical simulations to reinforce the results. For showing the applicability of our model in various fields, we illustrate the proposed test by applications to two real data sets for complete data case and two other data sets in the presence of right censored.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"135 1","pages":"330-353"},"PeriodicalIF":0.0,"publicationDate":"2020-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77984557","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}
In this paper we present coincidence, homotopy and normalization type results in the weak topology setting for general classes of Mönch type maps.
本文给出了Mönch类型映射的一般类的弱拓扑设置中的偶合、同伦和归一化类型结果。
{"title":"Epi Mönch type maps in the weak topology setting","authors":"D. O’Regan","doi":"10.22436/jnsa.013.06.02","DOIUrl":"https://doi.org/10.22436/jnsa.013.06.02","url":null,"abstract":"In this paper we present coincidence, homotopy and normalization type results in the weak topology setting for general classes of Mönch type maps.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"19 1","pages":"317-322"},"PeriodicalIF":0.0,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82712498","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}
In this paper, a Halpern type iterative scheme for finding a common element in the set of fixed points of generic 2generalized Bregman nonspreading mappings and the solution set of equilibrium problem have been proposed. We also prove that the sequence generated by the scheme converges strongly to the element in a real reflexive Banach space. Our results improve and generalize some announced results in the literature.
{"title":"Fixed point approximations of noncommutative generic 2-generalized Bregman nonspreading mappings with equilibriums","authors":"B. Ali, L. Y. Haruna","doi":"10.22436/jnsa.013.06.01","DOIUrl":"https://doi.org/10.22436/jnsa.013.06.01","url":null,"abstract":"In this paper, a Halpern type iterative scheme for finding a common element in the set of fixed points of generic 2generalized Bregman nonspreading mappings and the solution set of equilibrium problem have been proposed. We also prove that the sequence generated by the scheme converges strongly to the element in a real reflexive Banach space. Our results improve and generalize some announced results in the literature.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"38 1","pages":"303-316"},"PeriodicalIF":0.0,"publicationDate":"2020-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77340302","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}
In the present article, we study the solvability of a class of fractional functional integro-differential equations of the CaputoKatugampola type. The existence of solutions is investigated under sufficient conditions as well as the assumptions which guarantee the uniqueness of the solution is explained. Also, we examine the continuous dependence of the solution on the initial condition, the lag function 0 6 ψ(t) 6 t, and the considered nonlinear functional. We give an example to explain our results. The outcomes in this paper extend the results developed by El-Sayed et al. in [A. M. A. El-Sayed, R. G. Ahmed, J. Nonlinear Sci. Appl., 13 (2020), 1–8], recently.
本文研究了一类CaputoKatugampola型分数阶泛函积分微分方程的可解性。在充分条件下研究了解的存在性，并给出了保证解的唯一性的假设。此外，我们还研究了解对初始条件的连续依赖，滞后函数0 6 ψ(t) 6 t，以及所考虑的非线性泛函。我们给出一个例子来解释我们的结果。本文的结果扩展了El-Sayed等人在[A.]M. A. El-Sayed, R. G. Ahmed, J.非线性科学达成。生态学报，13 (2020)，1-8 [j]。
{"title":"Caputo-Katugampola fractional Volterra functional differential equations with a vanishing lag function","authors":"M. I. Youssef","doi":"10.22436/jnsa.013.05.06","DOIUrl":"https://doi.org/10.22436/jnsa.013.05.06","url":null,"abstract":"In the present article, we study the solvability of a class of fractional functional integro-differential equations of the CaputoKatugampola type. The existence of solutions is investigated under sufficient conditions as well as the assumptions which guarantee the uniqueness of the solution is explained. Also, we examine the continuous dependence of the solution on the initial condition, the lag function 0 6 ψ(t) 6 t, and the considered nonlinear functional. We give an example to explain our results. The outcomes in this paper extend the results developed by El-Sayed et al. in [A. M. A. El-Sayed, R. G. Ahmed, J. Nonlinear Sci. Appl., 13 (2020), 1–8], recently.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"94 1","pages":"293-302"},"PeriodicalIF":0.0,"publicationDate":"2020-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91064400","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}
In this paper, we study the split common fixed point problem in reflexive Banach spaces, we obtain a strong convergence theorem for approximating a solution of the split common fixed point problem for Bregman demigeneralized mapping. Our result extend and improve important recent results announced by many authors.
{"title":"Split common fixed point problem for Bregman demigeneralized mappings in Banach spaces with applications","authors":"B. Ali, G. C. Ugwunnadi, M. S. Lawan","doi":"10.22436/jnsa.013.05.04","DOIUrl":"https://doi.org/10.22436/jnsa.013.05.04","url":null,"abstract":"In this paper, we study the split common fixed point problem in reflexive Banach spaces, we obtain a strong convergence theorem for approximating a solution of the split common fixed point problem for Bregman demigeneralized mapping. Our result extend and improve important recent results announced by many authors.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"15 1","pages":"270-283"},"PeriodicalIF":0.0,"publicationDate":"2020-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75482382","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}
We introduce a new three-parameter model called the odd inverse Pareto exponential distribution which extends the exponential distribution and provides constant, decreasing, increasing, decreasing-increasing, upside-down bathtub and bathtub failure rate shapes. Some of its mathematical properties are derived. The maximum likelihood method is used to estimate the model parameters. The proposed model provides better fits over some existing distributions by means of two real data sets.
{"title":"A new three-parameter exponential distribution with applications in reliability and engineering","authors":"Maha A. Aldahlan, A. Afify","doi":"10.22436/jnsa.013.05.03","DOIUrl":"https://doi.org/10.22436/jnsa.013.05.03","url":null,"abstract":"We introduce a new three-parameter model called the odd inverse Pareto exponential distribution which extends the exponential distribution and provides constant, decreasing, increasing, decreasing-increasing, upside-down bathtub and bathtub failure rate shapes. Some of its mathematical properties are derived. The maximum likelihood method is used to estimate the model parameters. The proposed model provides better fits over some existing distributions by means of two real data sets.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"19 1","pages":"258-269"},"PeriodicalIF":0.0,"publicationDate":"2020-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76796211","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}
M. Mansour, H. Yousof, Wahid A. M. Shehata, M. Ibrahim
We present a new two parameter Burr XII distribution. The new density can be right skewed with no peak, unimodal-right skewed, left skewed and symmetric. The new failure rate can be decreasing, unimodal and increasing. Properties related to the new model are derived. Simple type copula-based construction is presented for deriving some new bivariate and multivariate type distributions. The maximum likelihood estimation, Anderson Darling estimation, right tail Anderson Darling estimation and left tail Anderson Darling estimation methods are used to estimate the model parameters. A new data set is analyzed for comparing estimations methods and the competitive models.
{"title":"A new two parameter Burr XII distribution: properties, copula, different estimation methods, and modeling acute bone cancer data","authors":"M. Mansour, H. Yousof, Wahid A. M. Shehata, M. Ibrahim","doi":"10.22436/jnsa.013.05.01","DOIUrl":"https://doi.org/10.22436/jnsa.013.05.01","url":null,"abstract":"We present a new two parameter Burr XII distribution. The new density can be right skewed with no peak, unimodal-right skewed, left skewed and symmetric. The new failure rate can be decreasing, unimodal and increasing. Properties related to the new model are derived. Simple type copula-based construction is presented for deriving some new bivariate and multivariate type distributions. The maximum likelihood estimation, Anderson Darling estimation, right tail Anderson Darling estimation and left tail Anderson Darling estimation methods are used to estimate the model parameters. A new data set is analyzed for comparing estimations methods and the competitive models.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"72 1","pages":"223-238"},"PeriodicalIF":0.0,"publicationDate":"2020-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83209178","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}
Let X be a real locally uniformly convex reflexive Banach space. Let T : X ⊇ D(T) → 2X and A : X ⊇ D(A) → 2X be maximal monotone operators such that T is of compact resolvents and A is strongly quasibounded, and C : X ⊇ D(C) → X∗ be a bounded and continuous operator with D(A) ⊆ D(C) or D(C) = U. The set U is a nonempty and open (possibly unbounded) subset of X. New degree mappings are constructed for operators of the type T +A+C. The operator C is neither pseudomonotone type nor defined everywhere. The theory for the case D(C) = U presents a new degree mapping for possibly unbounded U and both of these theories are new even when A is identically zero. New existence theorems are derived. The existence theorems are applied to prove the existence of a solution for a nonlinear variational inequality problem.
{"title":"Topological degree theories for continuous perturbations of resolvent compact maximal monotone operators, existence theorems and applications","authors":"Teffera M. Asfaw","doi":"10.22436/jnsa.013.05.02","DOIUrl":"https://doi.org/10.22436/jnsa.013.05.02","url":null,"abstract":"Let X be a real locally uniformly convex reflexive Banach space. Let T : X ⊇ D(T) → 2X and A : X ⊇ D(A) → 2X be maximal monotone operators such that T is of compact resolvents and A is strongly quasibounded, and C : X ⊇ D(C) → X∗ be a bounded and continuous operator with D(A) ⊆ D(C) or D(C) = U. The set U is a nonempty and open (possibly unbounded) subset of X. New degree mappings are constructed for operators of the type T +A+C. The operator C is neither pseudomonotone type nor defined everywhere. The theory for the case D(C) = U presents a new degree mapping for possibly unbounded U and both of these theories are new even when A is identically zero. New existence theorems are derived. The existence theorems are applied to prove the existence of a solution for a nonlinear variational inequality problem.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"16 1","pages":"239-257"},"PeriodicalIF":0.0,"publicationDate":"2020-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88728023","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}
The purpose of this research is to explore a fixed point method to solve a class of functional equations, Tu = f, where T is a differential or an integral operator on a Sobolev space H2(Ω), where Ω is an open set in Rn. First, T is converted into a sum of I+ λA with λ > 0, where A is a continuous linear operator and I is identity mapping. Then it is shown that T is a contraction on the prescribed Sobolev space and norm of A is estimated on the prescribed Sobolev space. By means of the theory of inverse operator of I+ λA and by choosing the appropriate value of λ, the solution u of differential or integral operator is obtained. Some practical problems concerning the linear differential equation and Fredholm integral equation are solved by virtue of the fixed point method.
{"title":"A fixed point method to solve differential equation and Fredholm integral equation","authors":"E. Nyein, A. Zaw","doi":"10.22436/jnsa.013.04.05","DOIUrl":"https://doi.org/10.22436/jnsa.013.04.05","url":null,"abstract":"The purpose of this research is to explore a fixed point method to solve a class of functional equations, Tu = f, where T is a differential or an integral operator on a Sobolev space H2(Ω), where Ω is an open set in Rn. First, T is converted into a sum of I+ λA with λ > 0, where A is a continuous linear operator and I is identity mapping. Then it is shown that T is a contraction on the prescribed Sobolev space and norm of A is estimated on the prescribed Sobolev space. By means of the theory of inverse operator of I+ λA and by choosing the appropriate value of λ, the solution u of differential or integral operator is obtained. Some practical problems concerning the linear differential equation and Fredholm integral equation are solved by virtue of the fixed point method.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"31 1","pages":"205-211"},"PeriodicalIF":0.0,"publicationDate":"2020-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88236171","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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