scholarly journals Classical and Bayesian Inference of a Mixture of Bivariate Exponentiated Exponential Model

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Refah Alotaibi ◽  
Mervat Khalifa ◽  
Ehab M. Almetwally ◽  
Indranil Ghosh ◽  
Rezk. H.
Keyword(s):  
Exponential Model ◽  
Gaussian Copula ◽  
Estimation Methods ◽  
Model Parameters ◽  
Reliability Engineering ◽  
Bivariate Model ◽  
Conditional Moments ◽  
Bayesian Paradigm ◽  
Proposed Model ◽  
Two Parameters

Exponentiated exponential (EE) model has been used effectively in reliability, engineering, biomedical, social sciences, and other applications. In this study, we introduce a new bivariate mixture EE model with two parameters assuming two cases, independent and dependent random variables. We develop a bivariate mixture starting from two EE models assuming two cases, two independent and two dependent EE models. We study some useful statistical properties of this distribution, such as marginals and conditional distributions and product moments and conditional moments. In addition, we study a dependent case, a new mixture of the bivariate model based on EE distribution marginal with two parameters and with a bivariate Gaussian copula. Different methods of estimation for the model parameters are used both under the classical and under the Bayesian paradigm. Some simulation studies are presented to verify the performance of the estimation methods of the proposed model. To illustrate the flexibility of the proposed model, a real dataset is reanalyzed.

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.

ON CONSTRUCTION OF STOCHASTIC GENETIC NETWORKS BASED ON GENE EXPRESSION SEQUENCES

2005 ◽  
Vol 15 (04) ◽  
pp. 297-310 ◽  
Author(s):  
WAI-KI CHING ◽  
MICHAEL M. NG ◽  
ERIC S. FUNG ◽  
TATSUYA AKUTSU
Keyword(s):  
Gene Expression ◽  
Regulatory Networks ◽  
Expression Patterns ◽  
Boolean Networks ◽  
Genetic Regulatory Networks ◽  
Efficient Estimation ◽  
Estimation Methods ◽  
Series Data ◽  
Model Parameters ◽  
Proposed Model

Reconstruction of genetic regulatory networks from time series data of gene expression patterns is an important research topic in bioinformatics. Probabilistic Boolean Networks (PBNs) have been proposed as an effective model for gene regulatory networks. PBNs are able to cope with uncertainty, corporate rule-based dependencies between genes and discover the sensitivity of genes in their interactions with other genes. However, PBNs are unlikely to use directly in practice because of huge amount of computational cost for obtaining predictors and their corresponding probabilities. In this paper, we propose a multivariate Markov model for approximating PBNs and describing the dynamics of a genetic network for gene expression sequences. The main contribution of the new model is to preserve the strength of PBNs and reduce the complexity of the networks. The number of parameters of our proposed model is O(n2) where n is the number of genes involved. We also develop efficient estimation methods for solving the model parameters. Numerical examples on synthetic data sets and practical yeast data sequences are given to demonstrate the effectiveness of the proposed model.

scholarly journals On the Burr XII-moment exponential distribution

PLoS ONE ◽  
2021 ◽  
Vol 16 (2) ◽  
pp. e0246935
Author(s):  
Fiaz Ahmad Bhatti ◽  
G. G. Hamedani ◽  
Mustafa Ç. Korkmaz ◽  
Wenhui Sheng ◽  
Azeem Ali
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Estimation Methods ◽  
Model Parameters ◽  
Simulation Studies ◽  
Conditional Moments ◽  
Mathematical Properties ◽  
Lifetime Model ◽  
Anderson Darling ◽  
Von Mises

In this study, a new flexible lifetime model called Burr XII moment exponential (BXII-ME) distribution is introduced. We derive some of its mathematical properties including the ordinary moments, conditional moments, reliability measures and characterizations. We employ different estimation methods such as the maximum likelihood, maximum product spacings, least squares, weighted least squares, Cramer-von Mises and Anderson-Darling methods for estimating the model parameters. We perform simulation studies on the basis of the graphical results to see the performance of the above estimators of the BXII-ME distribution. We verify the potentiality of the BXII-ME model via monthly actual taxes revenue and fatigue life applications.

scholarly journals A Non-Invasive Procedure for Estimating the Exponential Model Parameters of Bypass Diodes in Photovoltaic Modules

Energies ◽  
2019 ◽  
Vol 12 (2) ◽  
pp. 303 ◽  
Author(s):  
Jeisson Vélez-Sánchez ◽  
Juan Bastidas-Rodríguez ◽  
Carlos Ramos-Paja ◽  
Daniel González Montoya ◽  
Luz Trejos-Grisales
Keyword(s):  
Invasive Procedure ◽  
Exponential Model ◽  
Model Parameters ◽  
Estimation Errors ◽  
Photovoltaic Modules ◽  
Non Invasive ◽  
Pv Module ◽  
Current Voltage ◽  
Pv Modules ◽  
Two Parameters

Bypass diodes (BDs) present in photovoltaic (PV) modules are represented by the exponential model, which requires two parameters: the inverse-saturation current ( I s a t , d b ) and the ideality factor ( η d b ). However, it is difficult to estimate those parameters since the terminals of the BDs are not isolated, hence there is only access to the series connection of the module BDs. This problem must be addressed since inaccurate BDs parameters could produce errors in the reproduction of the current-voltage (I-V) curves of commercial PV modules, which lead to wrong predictions of the power production. This paper proposes a non-invasive procedure to estimate I s a t , d b and η d b of the bypass diodes present in a PV module using two experimental I-V curves. One I-V curve is measured completely covering the submodule of the module whose BD will be parameterized; while the other I-V curve is measured without any shadow on the module. From those curves, the I-V curve of the BD is estimated and I s a t , d b and η d b are calculated by solving a system of two nonlinear equations. The proposed procedure is validated through simulations and experimental results considering a commercial PV module formed by three submodules, where the estimation errors in the reproduction of the BD I-V curve are less than 1% in the simulations and less than 10% in the experiments.

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 Estimation of Cough Peak Flow Using Cough Sounds

2018 ◽  
Author(s):  
Yasutaka Umayahara ◽  
Zu Soh ◽  
Kiyokazu Sekikawa ◽  
Toshihiro Kawae ◽  
Akira Otsuka ◽  
...  
Keyword(s):  
Evaluation Method ◽  
Peak Flow ◽  
Absolute Error ◽  
Face Mask ◽  
Exponential Model ◽  
Estimation Accuracy ◽  
Model Parameters ◽  
Proposed Model ◽  
The Face ◽  
And Gender

Cough peak flow (CPF) is a measurement to evaluate the risk of cough dysfunction and can be measured using various devices, such as spirometers. However, complex device setup and the face mask required to be firmly attached to the mouth impose burdens on both patients and their caregivers. Therefore, this study develops a novel cough strength evaluation method using cough sounds. This paper presents an exponential model to estimate CPF from the cough peak sound pressure level (CPSL). We investigated the relationship between cough sounds and cough flows and the effects of a measurement condition of cough sound, microphone type, and participant’s height and gender on CPF estimation accuracy. The results confirmed that the proposed model estimated CPF with a high accuracy. The absolute error between CPFs and estimated CPFs were significantly lower when the microphone distance from the participant’s mouth was within 30 cm than when the distance exceeded 30 cm. Analysis of the model parameters showed that the estimation accuracy was not affected by participant’s height or gender. These results indicate that the proposed model has the potential to improve the feasibility of measuring and assessing CPF.

scholarly journals TOPP LEONE WEIBULL LOMAX DISTRIBUTION: PROPERTIES, REGRESSION MODEL AND APPLICATIONS

2021 ◽  
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Muhammad Arslan Nasir ◽  
Christophe Chesneau ◽  
Jamal Abdul Nasir ◽  
...  
Keyword(s):  
Regression Model ◽  
Stochastic Ordering ◽  
Quantile Function ◽  
Model Parameters ◽  
Data Sets ◽  
Lomax Distribution ◽  
Conditional Moments ◽  
Estimated Parameters ◽  
Proposed Model ◽  
Probability Weighted Moment

A new four-parameter lifetime distribution (called the Topp Leone Weibull-Lomax distribution) is proposed in this paper. Different mathematical properties of the proposed distribution were studied which include quantile function, ordinary and incomplete moments, probability weighted moment, conditional moments, order statistics, stochastic ordering, and stress-strength reliability parameter. The regression model and the residual analysis for the proposed model were also carried out. The model parameters were estimated by using the maximum likelihood criterion and the behaviour of these estimated parameters were examined by conducting a simulation study. The importance and flexibility of the proposed distribution have been proved empirically by using four separate data sets.

Modeling the Recovery from Depressive Illness by an Exponential Model with Mixed Effects

2000 ◽  
Vol 39 (01) ◽  
pp. 12-15 ◽  
Author(s):  
T. Friede ◽  
F. Miller ◽  
M. Kieser
Keyword(s):  
Exponential Model ◽  
Depressive Illness ◽  
Mixed Effects ◽  
Controlled Study ◽  
Model Parameters ◽  
Rating Score ◽  
Recovery Curves ◽  
Antidepressant Treatments ◽  
Proposed Model ◽  
Treatment Of Depression

Abstract:In clinical trials of antidepressant treatments, a depression rating score is usually measured at several points of time for each patient. We propose an approach to fit data from this type of clinical trial using an exponential mixed-effects model. Compared to previous proposals, this approach has the advantage that individual recovery curves are fitted rather than curves of means. Furthermore, no artificial fixing of model parameters is needed as in other approaches. The flexibility of the proposed model is shown for various situations. The approach is illustrated by an example from a placebo-controlled study for the treatment of depression with St. John’s Wort (Hypericum perforatum).

scholarly journals The Inverse-Power Logistic-Exponential Distribution: Properties, Estimation Methods, and Application to Insurance Data

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2060
Author(s):  
Mashail M. AL Sobhi
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Weighted Least Squares ◽  
Estimation Methods ◽  
Inverse Power ◽  
Model Parameters ◽  
Proposed Model ◽  
Anderson Darling ◽  
Von Mises ◽  
Insurance Data

The present paper proposes a new distribution called the inverse power logistic exponential distribution that extends the inverse Weibull, inverse logistic exponential, inverse Rayleigh, and inverse exponential distributions. The proposed model accommodates symmetrical, right-skewed, left-skewed, reversed-J-shaped, and J-shaped densities and increasing, unimodal, decreasing, reversed-J-shaped, and J-shaped hazard rates. We derive some mathematical properties of the proposed model. The model parameters were estimated using five estimation methods including the maximum likelihood, Anderson–Darling, least-squares, Cramér–von Mises, and weighted least-squares estimation methods. The performance of these estimation methods was assessed by a detailed simulation study. Furthermore, the flexibility of the introduced model was studied using an insurance real dataset, showing that the proposed model can be used to fit the insurance data as compared with twelve competing models.

scholarly journals Neutrosophic Exponential Distribution: Modeling and Applications for Complex Data Analysis

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Wen-Qi Duan ◽  
Zahid Khan ◽  
Muhammad Gulistan ◽  
Adnan Khurshid
Keyword(s):  
Exponential Distribution ◽  
Exponential Model ◽  
Complex Data ◽  
Reliability Engineering ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Method Of Maximum Likelihood ◽  
Wide Range ◽  
Larger Sample ◽  
Complex Dataset

The exponential distribution has always been prominent in various disciplines because of its wide range of applications. In this work, a generalization of the classical exponential distribution under a neutrosophic environment is scarcely presented. The mathematical properties of the neutrosophic exponential model are described in detail. The estimation of a neutrosophic parameter by the method of maximum likelihood is discussed and illustrated with examples. The suggested neutrosophic exponential distribution (NED) model involves the interval time it takes for certain particular events to occur. Thus, the proposed model may be the most widely used statistical distribution for the reliability problems. For conceptual understanding, a wide range of applications of the NED in reliability engineering is given, which indicates the circumstances under which the distribution is suitable. Furthermore, a simulation study has been conducted to assess the performance of the estimated neutrosophic parameter. Simulated results show that imprecise data with a larger sample size efficiently estimate the unknown neutrosophic parameter. Finally, a complex dataset on remission periods of cancer patients has been analyzed to identify the importance of the proposed model for real-world case studies.

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