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Full-Text Articles in Mathematics
Predicting The Winning Percentage Of Limited-Overs Cricket Using The Pythagorean Formula, Hasika K. W. Senevirathne, Ananda B.W. Manage
Predicting The Winning Percentage Of Limited-Overs Cricket Using The Pythagorean Formula, Hasika K. W. Senevirathne, Ananda B.W. Manage
Mathematics & Statistics Faculty Publications
The Pythagorean Win-Loss formula can be effectively used to estimate winning percentages for sporting events. This formula was initially developed by baseball statistician Bill James and later was extended by other researchers to sports such as football, basketball, and ice hockey. Although one can calculate actual winning percentages based on the outcomes of played games, that approach does not take into account the margin of victory. The key benefit of the Pythagorean formula is its utilization of actual average runs scored and actual average runs allowed. This article presents the application of the Pythagorean Win-Loss formula to two different types …
Markov Chain Epidemic Models And Parameter Estimation, Oluwatobiloba Ige
Markov Chain Epidemic Models And Parameter Estimation, Oluwatobiloba Ige
Theses, Dissertations and Capstones
Over the years, various parts of the world have experienced disease outbreaks. Mathematical models are used to describe these outbreaks. We study the transmission of disease in simple cases of disease outbreaks by using compartmental models with Markov chains. First, we explore the formulation of compartmental SIS (Susceptible-Infectious-Susceptible) and SIR (Susceptible-Infectious-Recovered) disease models. These models are the basic building blocks of other compartmental disease models. Second, we build SIS and SIR disease models using both discrete and continuous time Markov chains. In discrete time models, transmission occurs at fixed time steps, and in continuous time models, transmission may occur at …
Critical Fault-Detecting Time Evaluation In Software With Discrete Compound Poisson Models, Min-Hsiung Hsieh, Shuen-Lin Jeng, Paul Kvam
Critical Fault-Detecting Time Evaluation In Software With Discrete Compound Poisson Models, Min-Hsiung Hsieh, Shuen-Lin Jeng, Paul Kvam
Department of Math & Statistics Faculty Publications
Software developers predict their product’s failure rate using reliability growth models that are typically based on nonhomogeneous Poisson (NHP) processes. In this article, we extend that practice to a nonhomogeneous discrete-compound Poisson process that allows for multiple faults of a system at the same time point. Along with traditional reliability metrics such as average number of failures in a time interval, we propose an alternative reliability index called critical fault-detecting time in order to provide more information for software managers making software quality evaluation and critical market policy decisions. We illustrate the significant potential for improved analysis using wireless failure …
Type I General Exponential Class Of Distributions, Gholamhossein G. Hamedani, Haitham M. Yousof, Mahdi Rasekhi, Morad Alizadeh, Seyed Morteza Najibi
Type I General Exponential Class Of Distributions, Gholamhossein G. Hamedani, Haitham M. Yousof, Mahdi Rasekhi, Morad Alizadeh, Seyed Morteza Najibi
Mathematics, Statistics and Computer Science Faculty Research and Publications
We introduce a new family of continuous distributions and study the mathematical properties of the new family. Some useful characterizations based on the ratio of two truncated moments and hazard function are also presented. We estimate the model parameters by the maximum likelihood method and assess its performance based on biases and mean squared errors in a simulation study framework.
On The Mixtures Of Weibull And Pareto (Iv) Distribution: An Alternative To Pareto Distribution, I. Ghosh, Gholamhossein G. Hamedani, Naveen K. Bansal, Mehdi Maadooliat
On The Mixtures Of Weibull And Pareto (Iv) Distribution: An Alternative To Pareto Distribution, I. Ghosh, Gholamhossein G. Hamedani, Naveen K. Bansal, Mehdi Maadooliat
Mathematics, Statistics and Computer Science Faculty Research and Publications
Finite mixture models have provided a reasonable tool to model various types of observed phenomena, specially those which are random in nature. In this article, a finite mixture of Weibull and Pareto (IV) distribution is considered and studied. Some structural properties of the resulting model are discussed including estimation of the model parameters via expectation maximization (EM) algorithm. A real-life data application exhibits the fact that in certain situations, this mixture model might be a better alternative than the rival popular models.
Mechanistic Plug-And-Play Models For Understanding The Impact Of Control And Climate On Seasonal Dengue Dynamics In Iquitos, Peru, Nathan Levick
Mechanistic Plug-And-Play Models For Understanding The Impact Of Control And Climate On Seasonal Dengue Dynamics In Iquitos, Peru, Nathan Levick
Mathematics & Statistics ETDs
Dengue virus is a mosquito-borne multi-serotype disease whose dynamics are not precisely understood despite half of the world’s human population being at risk of infection. A recent dataset of dengue case reports from an isolated Amazonian city— Iquitos, Peru—provides a unique opportunity to assess dengue dynamics in a simpli- fied setting. Ten years of clinical surveillance data reveal a specific pattern: two novel serotypes, in turn, invaded and exclusively dominated incidence over several seasonal cycles, despite limited intra-annual variation in climate conditions. Together with mechanistic mathematical models, these data can provide an improved understand- ing of the nonlinear interactions between …
Another Generalized Transmuted Family Of Distributions: Properties And Applications, Faton Merovci, Morad Alizadeh, Gholamhossein Hamedani
Another Generalized Transmuted Family Of Distributions: Properties And Applications, Faton Merovci, Morad Alizadeh, Gholamhossein Hamedani
Mathematics, Statistics and Computer Science Faculty Research and Publications
We introduce and study general mathematical properties of a new generator of continuous distributions with two extra parameters called the Another generalized transmuted family of distributions. We present some special models. We investigate the asymptotes and shapes. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. We obtain explicit expressions for the ordinary and incomplete moments and generating functions, Bonferroni and Lorenz curves, asymptotic distribution of the extreme values, Shannon and Renyi entropies and order statistics, which hold for any baseline model, certain characterisations are presented. Further, we …
Generalized Transmuted Family Of Distributions: Properties And Applications, Morad Alizadeh, Faton Merovci, Gholamhossein G. Hamedani
Generalized Transmuted Family Of Distributions: Properties And Applications, Morad Alizadeh, Faton Merovci, Gholamhossein G. Hamedani
Mathematics, Statistics and Computer Science Faculty Research and Publications
We introduce and study general mathematical properties of a new generator of continuous distributions with two extra parameters called the Generalized Transmuted Family of Distributions. We investigate the shapes and present some special models. The new density function can be expressed as a linear combination of exponentiated densities in terms of the same baseline distribution. We obtain explicit expressions for the ordinary and incomplete moments and generating function, Bonferroni and Lorenz curves, asymptotic distribution of the extreme values, Shannon and R´enyi entropies and order statistics, which hold for any baseline model. Further, we introduce a bivariate extension of the new …
Statistical Models For Hot Electron Degradation In Nano-Scaled Mosfet Devices, Suk Joo Bae, Seong-Joon Kim, Way Kuo, Paul H. Kvam
Statistical Models For Hot Electron Degradation In Nano-Scaled Mosfet Devices, Suk Joo Bae, Seong-Joon Kim, Way Kuo, Paul H. Kvam
Department of Math & Statistics Faculty Publications
In a MOS structure, the generation of hot carrier interface states is a critical feature of the item's reliability. On the nano-scale, there are problems with degradation in transconductance, shift in threshold voltage, and decrease in drain current capability. Quantum mechanics has been used to relate this decrease to degradation, and device failure. Although the lifetime, and degradation of a device are typically used to characterize its reliability, in this paper we model the distribution of hot-electron activation energies, which has appeal because it exhibits a two-point discrete mixture of logistic distributions. The logistic mixture presents computational problems that are …
Reliability Estimation Based On System Data With An Unknown Load Share Rule, Hyoungtae Kim, Paul H. Kvam
Reliability Estimation Based On System Data With An Unknown Load Share Rule, Hyoungtae Kim, Paul H. Kvam
Department of Math & Statistics Faculty Publications
We consider a multicomponent load-sharing system in which the failure rate of a given component depends on the set of working components at any given time. Such systems can arise in software reliability models and in multivariate failure-time models in biostatistics, for example. A load-share rule dictates how stress or load is redistributed to the surviving components after a component fails within the system. In this paper, we assume the load share rule is unknown and derive methods for statistical inference on load-share parameters based on maximum likelihood. Components with (individual) constant failure rates are observed in two environments: (1) …