An Advanced Discrete Model with Applications in Medical Science

2018 ◽  
Vol 09 (02) ◽  
pp. 1850001
Author(s):  
Bilal Ahmad Para ◽  
Tariq Rashid Jan
Keyword(s):  
Count Data ◽  
Discrete Model ◽  
Medical Science ◽  
Real Life ◽  
Medical Sciences ◽  
Proposed Model ◽  
Specific Parameter ◽  
Rate Functions ◽  
Two Parameter ◽  
New Distribution

In this paper, we introduce a new discrete model by compounding two parameter discrete Weibull distribution with Beta distribution of first kind. The proposed model can be nested to different compound distributions on specific parameter settings. The model is a good competitive for zero-inflated models. In addition, we present the basic properties of the new distribution and discuss unimodality, failure rate functions and index of dispersion. Finally, the model is examined with real-life count data from medical sciences to investigate the suitability of the proposed model.

scholarly journals Two-Parameter Nwikpe (TPAN) Distribution with Application

2021 ◽  
pp. 56-67
Author(s):  
Barinaadaa John Nwikpe ◽  
Isaac Didi Essi
Keyword(s):  
Goodness Of Fit ◽  
Continuous Distribution ◽  
Real Life ◽  
Moment Generating Function ◽  
Statistical Properties ◽  
Likelihood Method ◽  
Data Sets ◽  
Method Of Moment ◽  
Two Parameter ◽  
New Distribution

A new two-parameter continuous distribution called the Two-Parameter Nwikpe (TPAN) distribution is derived in this paper. The new distribution is a mixture of gamma and exponential distributions. A few statistical properties of the new probability distribution have been derived. The shape of its density for different values of the parameters has also been established.  The first four crude moments, the second and third moments about the mean of the new distribution were derived using the method of moment generating function. Other statistical properties derived include; the distribution of order statistics, coefficient of variation and coefficient of skewness. The parameters of the new distribution were estimated using maximum likelihood method. The flexibility of the Two-Parameter Nwikpe (TPAN) distribution was shown by fitting the distribution to three real life data sets. The goodness of fit shows that the new distribution outperforms the one parameter exponential, Shanker and Amarendra distributions for the data sets used for this study.

scholarly journals A New Extended Two-Parameter Distribution: Properties, Estimation Methods, and Applications in Medicine and Geology

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1578 ◽  
Author(s):  
Hazem Al-Mofleh ◽  
Ahmed Z. Afify ◽  
Noor Akma Ibrahim
Keyword(s):  
Estimation Method ◽  
Estimation Methods ◽  
Parameter Distribution ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Proposed Model ◽  
Rate Functions ◽  
The Mean ◽  
Modeling Data ◽  
Two Parameter

In this paper, a new two-parameter generalized Ramos–Louzada distribution is proposed. The proposed model provides more flexibility in modeling data with increasing, decreasing, J-shaped, and reversed-J shaped hazard rate functions. Several statistical properties of the model were derived. The unknown parameters of the new distribution were explored using eight frequentist estimation approaches. These approaches are important for developing guidelines to choose the best method of estimation for the model parameters, which would be of great interest to practitioners and applied statisticians. Detailed numerical simulations are presented to examine the bias and the mean square error of the proposed estimators. The best estimation method and ordering performance of the estimators were determined using the partial and overall ranks of all estimation methods for various parameter combinations. The performance of the proposed distribution is illustrated using two real datasets from the fields of medicine and geology, and both datasets show that the new model is more appropriate as compared to the Marshall–Olkin exponential, exponentiated exponential, beta exponential, gamma, Poisson–Lomax, Lindley geometric, generalized Lindley, and Lindley distributions, among others.

A new generalized version of Log-logistic distribution with applications in medical sciences and other applied fields

2018 ◽  
Vol 09 (05) ◽  
pp. 1850043
Author(s):  
Bilal Ahmad Para ◽  
Tariq Rashid Jan
Keyword(s):  
Real Life ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Medical Sciences ◽  
Real Life Data ◽  
Proposed Model ◽  
Asymptotic Confidence Intervals ◽  
Mc Simulation ◽  
Robust Measures ◽  
Applied Fields

In this paper, we studied a two-parameter transmuted model of Log-logistic distribution (LLD) using the quadratic rank transmutation map technique studied by Shaw and Buckley1 as a new survival model in medical sciences and other applied fields. Statistical properties of Transmuted LLD (TLLD) are discussed comprehensively. Robust measures of skewness and kurtosis of the proposed model have also been discussed along with graphical overview. The estimation of the model parameters is performed by Maximum Likelihood (ML) method followed by a Monte Carlo (MC) simulation procedure to investigate the performance of the ML estimators and the asymptotic confidence intervals of the parameters. Applications of the proposed model to real-life data are also presented.

scholarly journals Reliability Analysis of the New Exponential Inverted Topp–Leone Distribution with Applications

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1662
Author(s):  
Ahmed Sayed M. Metwally ◽  
Amal S. Hassan ◽  
Ehab M. Almetwally ◽  
B M Golam Kibria ◽  
Hisham M. Almongy
Keyword(s):  
Reliability Analysis ◽  
Confidence Intervals ◽  
Hazard Rate ◽  
Shape Parameter ◽  
Quantile Function ◽  
Proposed Model ◽  
Distribution Parameters ◽  
Rate Functions ◽  
New Distribution ◽  
Skewness And Kurtosis

The inverted Topp–Leone distribution is a new, appealing model for reliability analysis. In this paper, a new distribution, named new exponential inverted Topp–Leone (NEITL) is presented, which adds an extra shape parameter to the inverted Topp–Leone distribution. The graphical representations of its density, survival, and hazard rate functions are provided. The following properties are explored: quantile function, mixture representation, entropies, moments, and stress–strength reliability. We plotted the skewness and kurtosis measures of the proposed model based on the quantiles. Three different estimation procedures are suggested to estimate the distribution parameters, reliability, and hazard rate functions, along with their confidence intervals. Additionally, stress–strength reliability estimators for the NEITL model were obtained. To illustrate the findings of the paper, two real datasets on engineering and medical fields have been analyzed.

scholarly journals An extensive extension of exponentiated exponential distribution using alpha power transformation – statistical properties and applications in engineering science

2021 ◽  
Vol 17 (2) ◽  
pp. 59-74
Author(s):  
S. Qurat Ul Ain ◽  
K. Ul Islam Rather
Keyword(s):  
Exponential Distribution ◽  
Real Life ◽  
Statistical Properties ◽  
Data Sets ◽  
Alpha Power ◽  
Real Life Data ◽  
Proposed Model ◽  
Mean Variance ◽  
New Distribution ◽  
Extra Parameter

Abstract In this article, an extension of exponentiated exponential distribution is familiarized by adding an extra parameter to the parent distribution using alpha power technique. The new distribution obtained is referred to as Alpha Power Exponentiated Exponential Distribution. Various statistical properties of the proposed distribution like mean, variance, central and non-central moments, reliability functions and entropies have been derived. Two real life data sets have been applied to check the flexibility of the proposed model. The new density model introduced provides the better fit when compared with other related statistical models.

scholarly journals An Extension of Log-Logistic Distribution for Analyzing Survival Data

2020 ◽  
pp. 789-801
Author(s):  
Aliya Syed Malik ◽  
S.P. Ahmad
Keyword(s):  
Survival Data ◽  
Real Life ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Logistic Distribution ◽  
Data Sets ◽  
Alpha Power ◽  
Real Life Data ◽  
Proposed Model ◽  
New Distribution

In this paper, a new generalization of Log Logistic Distribution using Alpha Power Transformation is proposed. The new distribution is named Alpha Power Log-Logistic Distribution. A comprehensive account of some of its statistical properties are derived. The maximum likelihood estimation procedure is used to estimate the parameters. The importance and utility of the proposed model are proved empirically using two real life data sets.

scholarly journals The Exponential-Generalized Truncated Geometric (EGTG) Distribution: A New Lifetime Distribution

2017 ◽  
Vol 7 (1) ◽  
pp. 1 ◽  
Author(s):  
Mohieddine Rahmouni ◽  
Ayman Orabi
Keyword(s):  
Probability Distribution ◽  
Real Data ◽  
Lifetime Distribution ◽  
Data Sets ◽  
Application Study ◽  
Maximum Lifetime ◽  
Special Cases ◽  
Rate Functions ◽  
Two Parameter ◽  
New Distribution

This paper introduces a new two-parameter lifetime distribution, called the exponential-generalized truncated geometric (EGTG) distribution, by compounding the exponential with the generalized truncated geometric distributions. The new distribution involves two important known distributions, i.e., the exponential-geometric (Adamidis and Loukas, 1998) and the extended (complementary) exponential-geometric distributions (Adamidis et al., 2005; Louzada et al., 2011) in the minimum and maximum lifetime cases, respectively. General forms of the probability distribution, the survival and the failure rate functions as well as their properties are presented for some special cases. The application study is illustrated based on two real data sets.

scholarly journals A Weighted Poisson Distribution for Underdispersed Count Data

2021 ◽  
Vol 10 (4) ◽  
pp. 157
Author(s):  
Chedly Gelin Louzayadio ◽  
Rodnellin Onesime Malouata ◽  
Michel Diafouka Koukouatikissa
Keyword(s):  
Poisson Distribution ◽  
Count Data ◽  
Exponential Family ◽  
Discrete Distribution ◽  
Random Variable ◽  
Poisson Random Variable ◽  
Weighted Version ◽  
Poisson Variable ◽  
Two Parameter ◽  
New Distribution

In this paper, we present a new weighted Poisson distribution for modeling underdispersed count data. Weighted Poisson distribution occurs naturally in contexts where the probability that a particular observation of Poisson variable enters the sample gets multiplied by some non-negative weight function. Suppose a realization y of Y a Poisson random variable enters the investigator’s record with probability proportional to w(y): Clearly, the recorded y is not an observation on Y, but on the random variable Yw, which is said to be the weighted version of Y. This distribution a two-parameter is from the exponential family, it includes and generalizes the Poisson distribution by weighting. It is a discrete distribution that is more flexible than other weighted Poisson distributions that have been proposed for modeling underdispersed count data, for example, the extended Poisson distribution (Dimitrov and Kolev, 2000). We present some moment properties and we estimate its parameters. One classical example is considered to compare the fits of this new distribution with the extended Poisson distribution.

scholarly journals Harris Extended Power Lomax Distribution: Properties, Inference and Applications

2021 ◽  
Vol 10 (4) ◽  
pp. 77
Author(s):  
Adebisi Ade Ogunde ◽  
Victoria Eshomomoh Laoye ◽  
Ogbonnaya Nzie Ezichi ◽  
Kayode Oguntuase Balogun
Keyword(s):  
Time Distribution ◽  
Lorenz Curve ◽  
Life Time ◽  
Lomax Distribution ◽  
Proposed Model ◽  
Method Of Maximum Likelihood ◽  
Distribution Parameters ◽  
Rate Functions ◽  
New Distribution ◽  
Extended Power

In this work, we present a five-parameter life time distribution called Harris power Lomax (HPL)  distribution which is obtained by convoluting the Harris-G distribution and the Power Lomax distribution. When compared to the existing distributions, the new distribution exhibits a very flexible probability functions; which may be increasing, decreasing, J, and reversed J shapes been observed for the probability density and hazard rate functions. The structural properties of the new distribution are studied in detail which includes: moments, incomplete moment, Renyl entropy, order statistics, Bonferroni curve, and Lorenz curve etc. The HPL  distribution parameters are estimated by using the method of maximum likelihood. Monte Carlo simulation was carried out to investigate the performance of MLEs. Aircraft wind shield data and Glass fibre data applications demonstrate the applicability of the proposed model.

scholarly journals Equitable Domination in Vague Graphs With Application in Medical Sciences

2021 ◽  
Vol 9 ◽  
Author(s):  
Yongsheng Rao ◽  
Saeed Kosari ◽  
Zehui Shao ◽  
Xiaoli Qiang ◽  
Maryam Akhoundi ◽  
...  
Keyword(s):  
Biological Networks ◽  
Coding Theory ◽  
Social Systems ◽  
Medical Science ◽  
Real Life ◽  
Electrical Networks ◽  
Dominating Sets ◽  
Medical Sciences ◽  
Height Measurement ◽  
Wide Range

Considering all physical, biological, and social systems, fuzzy graph (FG) models serve the elemental processes of all natural and artificial structures. As the indeterminate information is an essential real-life problem, which is mostly uncertain, modeling the problems based on FGs is highly demanding for an expert. Vague graphs (VGs) can manage the uncertainty relevant to the inconsistent and indeterminate information of all real-world problems, in which FGs possibly will not succeed in bringing about satisfactory results. In addition, VGs are a very useful tool to examine many issues such as networking, social systems, geometry, biology, clustering, medical science, and traffic plan. The previous definition restrictions in FGs have made us present new definitions in VGs. A wide range of applications has been attributed to the domination in graph theory for several fields such as facility location problems, school bus routing, modeling biological networks, and coding theory. Concepts from domination also exist in problems involving finding the set of representatives, in monitoring communication and electrical networks, and in land surveying (e.g., minimizing the number of places a surveyor must stand in order to take the height measurement for an entire region). Hence, in this article, we introduce different concepts of dominating, equitable dominating, total equitable dominating, weak (strong) equitable dominating, equitable independent, and perfect dominating sets in VGs and also investigate their properties by some examples. Finally, we present an application in medical sciences to show the importance of domination in VGs.

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