scholarly journals A new approach for modeling covid-19 death data

2021 ◽  
pp. 1-9
Author(s):  
Muhammad Farooq ◽  
Qamar-uz-zaman ◽  
Muhammad Ijaz
Keyword(s):  
Probability Model ◽  
Developed Countries ◽  
Likelihood Method ◽  
Data Sets ◽  
Probability Models ◽  
New Approach ◽  
Proposed Model ◽  
Rate Functions ◽  
Day By Day ◽  
Death Data

The Covid-19 infections outbreak is increasing day by day and the mortality rate is increasing exponentially both in underdeveloped and developed countries. It becomes inevitable for mathematicians to develop some models that could define the rate of infections and deaths in a population. Although there exist a lot of probability models but they fail to model different structures (non-monotonic) of the hazard rate functions and also do not provide an adequate fit to lifetime data. In this paper, a new probability model (FEW) is suggested which is designed to evaluate the death rates in a Population. Various statistical properties of FEW have been screened out in addition to the parameter estimation by using the maximum likelihood method (MLE). Furthermore, to delineate the significance of the parameters, a simulation study is conducted. Using death data from Pakistan due to Covid-19 outbreak, the proposed model applications is studied and compared to that of other existing probability models such as Ex-W, W, Ex, AIFW, and GAPW. The results show that the proposed model FEW provides a much better fit while modeling these data sets rather than Ex-W, W, Ex, AIFW, and GAPW.

scholarly journals Truncated Akash distribution: properties and applications

2020 ◽  
Vol 9 (5) ◽  
pp. 179-184
Author(s):  
Kamlesh Kumar Shukla
Keyword(s):  
Maximum Likelihood ◽  
Coefficient Of Variation ◽  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Data Sets ◽  
Proposed Model ◽  
Rate Functions ◽  
Mean And Variance

In this paper, Truncated Akash distribution has been proposed. Its mean and variance have been derived. Nature of cumulative distribution and hazard rate functions have been derived and presented graphically. Its moments including Coefficient of Variation, Skenwness, Kurtosis and Index of dispersion have been derived. Maximum likelihood method of estimation has been used to estimate the parameter of proposed model. It has been applied on three data sets and compares its superiority over one parameter exponential, Lindley, Akash, Ishita and truncated Lindley distribution.

scholarly journals The extended odd family of probability distributions with practice to a submodel

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3855-3867 ◽  
Author(s):  
Hassan Bakouch ◽  
Christophe Chesneau ◽  
Muhammad Khan
Keyword(s):  
Heavy Tails ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Likelihood Method ◽  
Tuning Parameter ◽  
Data Sets ◽  
New Family ◽  
Rate Functions ◽  
Special Case ◽  
Family Of Distributions

In this paper, we introduce a new family of distributions extending the odd family of distributions. A new tuning parameter is introduced, with some connections to the well-known transmuted transformation. Some mathematical results are obtained, including moments, generating function and order statistics. Then, we study a special case dealing with the standard loglogistic distribution and the modifiedWeibull distribution. Its main features are to have densities with flexible shapes where skewness, kurtosis, heavy tails and modality can be observed, and increasing-decreasing-increasing, unimodal and bathtub shaped hazard rate functions. Estimation of the related parameters is investigated by the maximum likelihood method. We illustrate the usefulness of our extended odd family of distributions with applications to two practical data sets.

scholarly journals The Alpha Power Transformation Family: Properties and Applications

2019 ◽  
pp. 525-545 ◽  
Author(s):  
Mohamed E. Mead ◽  
Gauss M. Cordeiro ◽  
Ahmed Z. Afify ◽  
Hazem Al Mofleh
Keyword(s):  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Power Transformation ◽  
Data Sets ◽  
Alpha Power ◽  
Weibull Distributions ◽  
Exponentiated Weibull ◽  
Rate Functions ◽  
Modified Weibull

Mahdavi A. and Kundu D. (2017) introduced a family for generating univariate distributions called the alpha power transformation. They studied as a special case the properties of the alpha power transformed exponential distribution. We provide some mathematical properties of this distribution and define a four-parameter lifetime model called the alpha power exponentiated Weibull distribution. It generalizes some well-known lifetime models such as the exponentiated exponential, exponentiated Rayleigh, exponentiated Weibull and Weibull distributions. The importance of the new distribution comes from its ability to model monotone and non-monotone failure rate functions, which are quite common in reliability studies. We derive some basic properties of the proposed distribution including quantile and generating functions, moments and order statistics. The maximum likelihood method is used to estimate the model parameters. Simulation results investigate the performance of the estimates. We illustrate the importance of the proposed distribution over the McDonald Weibull, beta Weibull, modified Weibull, transmuted Weibull and exponentiated Weibull distributions by means of two real data sets.

scholarly journals Extended Odd Fréchet-G Family of Distributions

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Suleman Nasiru
Keyword(s):  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Data Sets ◽  
Data Set ◽  
New Class ◽  
New Family ◽  
Rate Functions ◽  
The Given ◽  
Family Of Distributions

The need to develop generalizations of existing statistical distributions to make them more flexible in modeling real data sets is vital in parametric statistical modeling and inference. Thus, this study develops a new class of distributions called the extended odd Fréchet family of distributions for modifying existing standard distributions. Two special models named the extended odd Fréchet Nadarajah-Haghighi and extended odd Fréchet Weibull distributions are proposed using the developed family. The densities and the hazard rate functions of the two special distributions exhibit different kinds of monotonic and nonmonotonic shapes. The maximum likelihood method is used to develop estimators for the parameters of the new class of distributions. The application of the special distributions is illustrated by means of a real data set. The results revealed that the special distributions developed from the new family can provide reasonable parametric fit to the given data set compared to other existing distributions.

scholarly journals A New Generalized Weighted Weibull Distribution

2019 ◽  
pp. 161-178 ◽  
Author(s):  
Salman Abbas ◽  
Gamze Ozal ◽  
Saman Hanif Shahbaz ◽  
Muhammad Qaiser Shahbaz
Keyword(s):  
Weibull Distribution ◽  
Generating Function ◽  
Probability Generating Function ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model

In this article, we present a new generalization of weighted Weibull distribution using Topp Leone family of distributions. We have studied some statistical properties of the proposed distribution including quantile function, moment generating function, probability generating function, raw moments, incomplete moments, probability, weighted moments, Rayeni and q th entropy. The have obtained numerical values of the various measures to see the eect of model parameters. Distribution of of order statistics for the proposed model has also been obtained. The estimation of the model parameters has been done by using maximum likelihood method. The eectiveness of proposed model is analyzed by means of a real data sets. Finally, some concluding remarks are given.

scholarly journals THE TRANSMUTED GAMMA-GOMPERTZ DISTRIBUTION

2020 ◽  
Vol 8 (10) ◽  
pp. 236-248
Author(s):  
Rwabi AzZwideen ◽  
Loai M. Al Zou’bi
Keyword(s):  
Maximum Likelihood ◽  
Order Statistics ◽  
Generating Function ◽  
Maximum Likelihood Method ◽  
Probability Model ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Gompertz Distribution ◽  
Proposed Model

This article introduces a four-parameter probability model which represents a gener- alization of the the Gamma-Gompertz distribution using the quadratic rank trans- mutation map. The proposed model is named the Transmuted Gamma-Gompertz distribution. We provide explicit expressions for its statistical properties, moment generating function, quantile function, the order statistics, the quantile function and the median. We estimate the parameters of the distribution using the maximum likelihood method of estimation.

scholarly journals Modeling Age at Menstrual Onset and Developing Menarcheal Life Table

2021 ◽  
Author(s):  
Brijesh P. Singh
Keyword(s):  
Life Table ◽  
Probability Model ◽  
Age Distribution ◽  
Real Data ◽  
Least Square ◽  
Age At Menarche ◽  
Data Sets ◽  
Menarcheal Age ◽  
Proposed Model ◽  
Demographic Indicator

Population scientists are generally developing mathematical models/techniques in demography and to provide brief explanation of extensive data sets. The prime objective of the present paper is to propose a probability model to illustrate the distribution of female’s age at first menstrual onset. Menarcheal age distribution is used to evaluate risk associated to reproductive issues and may be used as a demographic indicator of female fecundity. The suitability of proposed model is tested with the real data sets. Parameters of the proposed distribution have been estimated through least square estimation technique. It is observed that older female’s age at menarche is somewhat higher than the younger female’s age at menarche. Also we have constructed a life table for menarcheal age using a probability model. This life table is enable to provide expected duration of getting menarche for a girl of a particular age.

Empirical Probability Models to Predict Precipitation Levels over Puerto Rico Stations

2007 ◽  
Vol 135 (3) ◽  
pp. 877-890 ◽  
Author(s):  
Nazario D. Ramirez-Beltran ◽  
William K. M. Lau ◽  
Amos Winter ◽  
Joan M. Castro ◽  
Nazario Ramirez Escalante
Keyword(s):  
Puerto Rico ◽  
Maximum Likelihood ◽  
Probability Model ◽  
Initial Point ◽  
Likelihood Method ◽  
Programming Algorithm ◽  
Regression Equations ◽  
Probability Models ◽  
Empirical Probability ◽  
Minimum Number

Abstract A new algorithm is proposed to predict the level of rainfall (above normal, normal, and below normal) in Puerto Rico that relies on probability and empirical models. The algorithm includes a theoretical probability model in which parameters are expressed as regression equations containing observed meteorological variables. Six rainfall stations were used in this study to implement and assess the reliability of the models. The stations, located throughout Puerto Rico, have monthly records that extend back 101 yr. The maximum likelihood method is used to estimate the parameters of the empirical probability models. A variable selection (VS) algorithm identifies the minimum number of variables that maximize the correlation between predictors and a predictand. The VS algorithm is used to identify the initial point and the maximum likelihood is optimized by using the sequential quadratic programming algorithm. Ten years of cross validation were applied to the results from six stations. The proposed method outperforms both climatology and damped persistence models. Results suggest that the methodology implemented here can be used as a potential tool to predict the level of rainfall at any station located on a tropical island, assuming that at least 50 yr of monthly rainfall observations are available. Model analyses show that meteorological indices can be used to predict rainfall stages.

scholarly journals Nonparametric Modeling of Random Uncertainties for Dynamic Response of Mistuned Bladed Disks

2004 ◽  
Vol 126 (3) ◽  
pp. 610-618 ◽  
Author(s):  
E. Capiez-Lernout ◽  
C. Soize
Keyword(s):  
Probability Model ◽  
Nonparametric Model ◽  
Probability Models ◽  
Nonparametric Modeling ◽  
Modal Shape ◽  
New Approach ◽  
Nonlinear Elastodynamics ◽  
Optimization Principle ◽  
Random Character ◽  
Random Uncertainties

The random character of blade mistuning is a motivation to construct probability models of random uncertainties. Recently, a new approach known as a nonparametric model of random uncertainties, based on the entropy optimization principle, was introduced for modeling random uncertainties in linear and nonlinear elastodynamics. This paper presents an extension of this nonparametric model for vibration analysis of structures with cyclic geometry. In particular this probability model allows the blade eigenfrequencies uncertainties and the blade-modal-shape uncertainties to be modeled.

Regression trees with splitting based on changes of dependencies among covariates

2021 ◽  
Vol 25 (3) ◽  
pp. 687-710
Author(s):  
Mostafa Boskabadi ◽  
Mahdi Doostparast
Keyword(s):  
Regression Trees ◽  
Real Data ◽  
Data Sets ◽  
Monte Carlo Simulation Study ◽  
New Approach ◽  
Homogeneous Groups ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Regression Problems ◽  
Dependency Structures

Regression trees are powerful tools in data mining for analyzing data sets. Observations are usually divided into homogeneous groups, and then statistical models for responses are derived in the terminal nodes. This paper proposes a new approach for regression trees that considers the dependency structures among covariates for splitting the observations. The mathematical properties of the proposed method are discussed in detail. To assess the accuracy of the proposed model, various criteria are defined. The performance of the new approach is assessed by conducting a Monte-Carlo simulation study. Two real data sets on classification and regression problems are analyzed by using the obtained results.

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