scholarly journals On Statistical Development of Neutrosophic Gamma Distribution with Applications to Complex Data Analysis

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Zahid Khan ◽  
Afrah Al-Bossly ◽  
Mohammed M. A. Almazah ◽  
Fuad S. Alduais
Keyword(s):  
Data Analysis ◽  
Gamma Distribution ◽  
Real Data ◽  
Moment Generating Function ◽  
Complex Data ◽  
Gamma Model ◽  
Distributional Properties ◽  
Proposed Model ◽  
Quantifying Uncertainty ◽  
Statistical Development

In the absence of a correct distribution theory for complex data, neutrosophic algebra can be very useful in quantifying uncertainty. In applied data analysis, implementation of existing gamma distribution becomes inadequate for some applications when dealing with an imprecise, uncertain, or vague dataset. Most existing works have explored distributional properties of the gamma distribution under the assumption that data do not have any kind of indeterminacy. Yet, analytical properties of the gamma model for the more realistic setting when data involved uncertainties remain largely underdeveloped. This paper fills such a gap and develops the notion of neutrosophic gamma distribution (NGD). The proposed distribution represents a generalized structure of the existing gamma distribution. The basic distributional properties, including moments, shape coefficients, and moment generating function (MGF), are established. Several examples are considered to emphasize the relevance of the proposed NGD for dealing with circumstances with inadequate or ambiguous knowledge about the distributional characteristics. The estimation framework for treating vague parameters of the NGD is developed. The Monte Carlo simulation is implemented to examine the performance of the proposed model. The proposed model is applied to a real dataset for the purpose of dealing with inaccurate and vague statistical data. Results show that the NGD has better flexibility in handling real data over the conventional gamma distribution.

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 Transmutation of the two parameters Rayleigh distribution

2016 ◽  
Vol 4 (2) ◽  
pp. 95
Author(s):  
Ehsan Ullah ◽  
Mirza Shahzad
Keyword(s):  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Rayleigh Distribution ◽  
Least Square ◽  
Least Square Estimation ◽  
Proposed Model ◽  
Method Of Least Square ◽  
Two Parameters ◽  
Mean Variance

In this study, transmuted two parameters Rayleigh distribution is proposed using quadratic rank transmutation map. This proposed distribution is more flexible and versatile than two parameters Rayleigh distribution. Some properties of the proposed distribution are derived such as moments, moment generating function, mean, variance, median, quantile function, reliability, and hazard function. The parameter estimation is approached through the method of least square estimation. The th and joint order statistics are also derived for the proposed distribution. The application of proposed model illustrated and compared using real data.

The Lindley negative-binomial distribution: Properties, estimation and applications to lifetime data

2020 ◽  
Vol 70 (4) ◽  
pp. 917-934
Author(s):  
Muhammad Mansoor ◽  
Muhammad Hussain Tahir ◽  
Gauss M. Cordeiro ◽  
Sajid Ali ◽  
Ayman Alzaatreh
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Hazard Rate ◽  
Negative Binomial ◽  
Real Data ◽  
Moment Generating Function ◽  
Estimation Methods ◽  
Model Parameters ◽  
Proposed Model ◽  
Rate Functions

AbstractA generalization of the Lindley distribution namely, Lindley negative-binomial distribution, is introduced. The Lindley and the exponentiated Lindley distributions are considered as sub-models of the proposed distribution. The proposed model has flexible density and hazard rate functions. The density function can be decreasing, right-skewed, left-skewed and approximately symmetric. The hazard rate function possesses various shapes including increasing, decreasing and bathtub. Furthermore, the survival and hazard rate functions have closed form representations which make this model tractable for censored data analysis. Some general properties of the proposed model are studied such as ordinary and incomplete moments, moment generating function, mean deviations, Lorenz and Bonferroni curve. The maximum likelihood and the Bayesian estimation methods are utilized to estimate the model parameters. In addition, a small simulation study is conducted in order to evaluate the performance of the estimation methods. Two real data sets are used to illustrate the applicability of the proposed model.

scholarly journals Some Size Biased Probability Models for Adult out Migration Pattern

2020 ◽  
pp. 78-91
Author(s):  
Brijesh P. Singh ◽  
Sandeep Singh ◽  
Utpal Dhar Das ◽  
Gunjan Singh
Keyword(s):  
Maximum Likelihood ◽  
Poisson Distribution ◽  
Gamma Distribution ◽  
Real Data ◽  
Migration Pattern ◽  
Probability Models ◽  
Data Set ◽  
Proposed Model ◽  
Method Of Maximum Likelihood

In this paper an attempt has been made to inspect the distribution of the number of adult migrants from household through size biased probability models based on certain assumptions. Size Biased Poisson distribution compounded with various forms of Gamma distribution i.e. Gamma (1,θ) , Gamma (2,θ) and mixture of Gamma (1,θ) and Gamma (2,θ)  has been examined for some real data set of adult migration. The parameters of the proposed model have been estimated by method of maximum likelihood.  test indicates that the distributions proposed here are quite satisfactory to explain the pattern of adult out migration.

scholarly journals The alpha power Teissier distribution and its applications

2021 ◽  
Vol 16 (2) ◽  
pp. 2733-2747
Author(s):  
Joseph Thomas Eghwerido
Keyword(s):  
Data Analysis ◽  
Generating Function ◽  
Hazard Rate ◽  
Real Life ◽  
Probability Generating Function ◽  
Moment Generating Function ◽  
Rate Function ◽  
Alpha Power ◽  
Real Life Data ◽  
Proposed Model

Statistical distribution that represents the true characteristics of real-life data is paramount to data analysis. Thus, this study introduces a tractable alpha power Teissier distribution (APOT). Some statistical properties of the proposed model like moments, probability generating function, moment generating function and order statistic were examined. The shape of the hazard rate and survival functions were investigated. The shapes of the hazard rate function indicated increasing, decreasing, J-shaped and bathtub shapes. The results of the data analysis indicated that the APOT model performed better when compared to some existing classical statistical distributions.

scholarly journals A Bimodal Extension of the Generalized Gamma Distribution

2015 ◽  
Vol 38 (2) ◽  
pp. 353-370 ◽  
Author(s):  
Mehmet Niyazi Çankaya ◽  
Yakup Murat Bulut ◽  
Fatma Zehra Dogru ◽  
Olcay Arslan
Keyword(s):  
Maximum Likelihood ◽  
Gamma Distribution ◽  
Real Data ◽  
Generalized Gamma Distribution ◽  
Generalized Gamma ◽  
Distributional Properties ◽  
Modeling Data ◽  
New Distribution

A bimodal extension of the generalized gamma distribution is proposed by using a mixing approach. Some distributional properties of the new distribution are investigated. The maximum likelihood (ML) estimators for the parameters of the new distribution are obtained. Real data examples are given to show the strength of the new distribution for modeling data.

scholarly journals Statistical Indicators of the Scientific Publications Importance: A Stochastic Model and Critical Look

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 713
Author(s):  
Lev B. Klebanov ◽  
Yulia V. Kuvaeva ◽  
Zeev E. Volkovich
Keyword(s):  
Data Analysis ◽  
Stochastic Model ◽  
Real Data ◽  
Scientific Publication ◽  
Hirsch Index ◽  
Citation Distribution ◽  
Scientific Publications ◽  
Proposed Model ◽  
Statistical Indicators

A model of scientific citation distribution is given. We apply it to understand the role of the Hirsch index as an indicator of scientific publication importance in Mathematics and some related fields. The proposed model is based on a generalization of such well-known distributions as geometric and Sibuya laws. Real data analysis of the Hirsch index and corresponding citation numbers is given.

scholarly journals The Flexible Weibull Extension-Burr XII Distribution: Model, Properties and Applications

2020 ◽  
pp. 447-460
Author(s):  
Rania M. Kamal ◽  
Moshira A. Ismail
Keyword(s):  
Additive Model ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Distribution Model ◽  
Data Set ◽  
Burr Xii Distribution ◽  
Proposed Model ◽  
The Moment ◽  
Modified Weibull

This paper is devoted to study a new four- parameter additive model. The newly suggested model is referred to as the flexible Weibull extension-Burr XII distribution. It is derived by considering a serial system with one component following a flexible Weibull extension distribution and another following a Burr XII distribution. The usefulness of the model stems from the flexibility of its failure rate which accommodates bathtub and modified bathtub among other risk patterns. These two patterns have been widely accepted in several fields, especially reliability and engineering fields. In addition, the importance of the new distribution is that it includes new sub-models which are not known in the literature. Some statistical properties of the proposed distribution such as quantile function, the mode, the rth moment, the moment generating function and the order statistics are discussed. Moreover, the method of maximum likelihood is used to estimate the parameters of the model. Also, to evaluate the performance of the estimators, a simulation study is carried out. Finally, the performance of the proposed distribution is compared through a real data set to some well-known distributions including the new modified Weibull, the additive Burr and the additive Weibull distributions. It is shown that the proposed model provides the best fit for the used real data set.  

scholarly journals Type II Exponentiated Half-Logistic-Topp-Leone-G Power Series Class of Distributions with Applications

2021 ◽  
pp. 885-909
Author(s):  
Thatayaone Moakofi ◽  
Broderick Oluyede ◽  
Fastel Chipepa
Keyword(s):  
Maximum Likelihood ◽  
Power Series ◽  
Real Data ◽  
Moment Generating Function ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
Type Ii ◽  
Nested Models ◽  
New Class ◽  
Proposed Model

This paper aims to develop a new class of distributions, namely, type II exponentiated half-logistic Topp-Leone power series (TIIEHL-TL-GPS) class of distributions. Some important properties including moments, quantiles, moment generating function, entropy and maximum likelihood estimates are derived. A simulation is conducted study to evaluate the consistency of the maximum likelihood estimates. We also present three real data examples to illustrate the usefulness of the new class of distributions. Results shows that the proposed model performs better than nested and several non-nested models on selected data sets

THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

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