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.

scholarly journals The Weibull Birnbaum-Saunders Distribution And Its Applications

2020 ◽  
Vol 9 (1) ◽  
pp. 61-81
Author(s):  
Lazhar BENKHELIFA
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Reliability Estimation ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model ◽  
Modeling Data

A new lifetime model, with four positive parameters, called the Weibull Birnbaum-Saunders distribution is proposed. The proposed model extends the Birnbaum-Saunders distribution and provides great flexibility in modeling data in practice. Some mathematical properties of the new distribution are obtained including expansions for the cumulative and density functions, moments, generating function, mean deviations, order statistics and reliability. Estimation of the model parameters is carried out by the maximum likelihood estimation method. A simulation study is presented to show the performance of the maximum likelihood estimates of the model parameters. The flexibility of the new model is examined by applying it to two real data sets.

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 Remaining useful life prediction of cylinder liner based on nonlinear degradation model

2021 ◽  
Vol 24 (1) ◽  
pp. 62-69
Author(s):  
Jianxiong Kang ◽  
Yanjun Lu ◽  
Bin Zhao ◽  
Hongbo Luo ◽  
Jiacheng Meng ◽  
...  
Keyword(s):  
Estimation Method ◽  
Cylinder Liner ◽  
Likelihood Estimation ◽  
Remaining Useful Life ◽  
Model Parameters ◽  
Operational Environment ◽  
Unknown Parameters ◽  
Degradation Model ◽  
Proposed Model ◽  
Useful Life

In order to effectively monitor the wear and predict the life of cylinder liner, a nonlinear degradation model with multi-source uncertainty based on Wiener process is established to evaluate the remaining useful life (RUL) of cylinder liner wear. Due to complex service performance of cylinder liner, the uncertainty of operational environment and working conditions of cylinder liner wear are considered into the model by a random function. The probability density function (PDF) formula of RUL is derived, and the maximum likelihood estimation method is adopted to estimate the unknown parameters of PDF. Considering the evaluated parameters as the initial values, the model parameters are updated adaptively, and an adaptive PDF is obtained. Furthermore, the proposed model is compared with two classical degradation models. The results show that the proposed model has a good performance for predicting the life, and the error is within 5%. The method can provide a reference for condition monitoring of cylinder liner wear.

scholarly journals A New Two-Parameter Burr-Hatke Distribution: Properties and Bayesian and Non-Bayesian Inference with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Ahmed Z. Afify ◽  
Hassan M. Aljohani ◽  
Abdulaziz S. Alghamdi ◽  
Ahmed M. Gemeay ◽  
Abdullah M. Sarg
Keyword(s):  
Real Life ◽  
Estimation Methods ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Bayesian Techniques ◽  
Bathtub Shape ◽  
Mathematical Properties ◽  
Squared Error ◽  
And Behavior ◽  
Two Parameter

This article introduces a two-parameter flexible extension of the Burr-Hatke distribution using the inverse-power transformation. The failure rate of the new distribution can be an increasing shape, a decreasing shape, or an upside-down bathtub shape. Some of its mathematical properties are calculated. Ten estimation methods, including classical and Bayesian techniques, are discussed to estimate the model parameters. The Bayes estimators for the unknown parameters, based on the squared error, general entropy, and linear exponential loss functions, are provided. The ranking and behavior of these methods are assessed by simulation results with their partial and overall ranks. Finally, the flexibility of the proposed distribution is illustrated empirically using two real-life datasets. The analyzed data shows that the introduced distribution provides a superior fit than some important competing distributions such as the Weibull, Fréchet, gamma, exponential, inverse log-logistic, inverse weighted Lindley, inverse Pareto, inverse Nakagami-M, and Burr-Hatke distributions.

scholarly journals Selection of Efficient Parameter Estimation Method for Two-Parameter Weibull Distribution

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Mohammed M. A. Almazah ◽  
Muhammad Ismail
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Mean Square Error ◽  
Estimation Method ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Model Parameters ◽  
Mean Square ◽  
Two Parameter

Several studies have considered various scheduling methods and reliability functions to determine the optimum maintenance time. These methods and functions correspond to the lowest cost by using the maximum likelihood estimator to evaluate the model parameters. However, this paper aims to estimate the parameters of the two-parameter Weibull distribution (α, β). The maximum likelihood estimation method, modified linear exponential loss function, and Wyatt-based regression method are used for the estimation of the parameters. Minimum mean square error (MSE) criterion is used to evaluate the relative efficiency of the estimators. The comparison of the different parameter estimation methods is conducted, and the efficiency of these methods is observed, both mathematically and experimentally. The simulation study is conducted for comparison of samples sizes (10, 50, 100, 150) based on the mean square error (MSE). It is concluded that the maximum likelihood method was found to be the most efficient method for all sample sizes used in the research because it achieved the least MSE compared with other methods.

scholarly journals A modified truncated distribution for modeling the heavy tail, engineering and environmental sciences data

PLoS ONE ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. e0249001
Author(s):  
Ahtasham Gul ◽  
Muhammad Mohsin ◽  
Muhammad Adil ◽  
Mansoor Ali
Keyword(s):  
Hazard Function ◽  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Cumulative Distribution ◽  
Statistical Characteristics ◽  
Model Parameters ◽  
Truncated Distribution ◽  
Unknown Parameters ◽  
Proposed Model

Truncated models are imperative to efficiently analyze the finite data that we observe in almost all the real life situations. In this paper, a new truncated distribution having four parameters named Weibull-Truncated Exponential Distribution (W-TEXPD) is developed. The proposed model can be used as an alternative to the Exponential, standard Weibull and shifted Gamma-Weibull and three parameter Weibull distributions. The statistical characteristics including cumulative distribution function, hazard function, cumulative hazard function, central moments, skewness, kurtosis, percentile and entropy of the proposed model are derived. The maximum likelihood estimation method is employed to evaluate the unknown parameters of the W-TEXPD. A simulation study is also carried out to assess the performance of the model parameters. The proposed probability distribution is fitted on five data sets from different fields to demonstrate its vast application. A comparison of the proposed model with some extant models is given to justify the performance of the W-TEXPD.

An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications

2020 ◽  
Vol 70 (4) ◽  
pp. 953-978
Author(s):  
Mustafa Ç. Korkmaz ◽  
G. G. Hamedani
Keyword(s):  
Hazard Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Quantile Function ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Lorenz Curves ◽  
Proposed Model ◽  
New Distribution

AbstractThis paper proposes a new extended Lindley distribution, which has a more flexible density and hazard rate shapes than the Lindley and Power Lindley distributions, based on the mixture distribution structure in order to model with new distribution characteristics real data phenomena. Its some distributional properties such as the shapes, moments, quantile function, Bonferonni and Lorenz curves, mean deviations and order statistics have been obtained. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. Different estimation procedures have been employed to estimate the unknown parameters and their performances are compared via Monte Carlo simulations. The flexibility and importance of the proposed model are illustrated by two real data sets.

scholarly journals Experimental Verification of Real-Time Flow-Rate Estimations in a Tilting-Ladle-Type Automatic Pouring Machine

2021 ◽  
Vol 11 (15) ◽  
pp. 6701
Author(s):  
Yuta Sueki ◽  
Yoshiyuki Noda
Keyword(s):  
Real Time ◽  
Molten Metal ◽  
Flow Rate ◽  
Kalman Filters ◽  
Estimation Method ◽  
Estimation Methods ◽  
Liquid Volume ◽  
Model Parameters ◽  
Rate Estimation ◽  
Time Flow

This paper discusses a real-time flow-rate estimation method for a tilting-ladle-type automatic pouring machine used in the casting industry. In most pouring machines, molten metal is poured into a mold by tilting the ladle. Precise pouring is required to improve productivity and ensure a safe pouring process. To achieve precise pouring, it is important to control the flow rate of the liquid outflow from the ladle. However, due to the high temperature of molten metal, directly measuring the flow rate to devise flow-rate feedback control is difficult. To solve this problem, specific flow-rate estimation methods have been developed. In the previous study by present authors, a simplified flow-rate estimation method was proposed, in which Kalman filters were decentralized to motor systems and the pouring process for implementing into the industrial controller of an automatic pouring machine used a complicatedly shaped ladle. The effectiveness of this flow rate estimation was verified in the experiment with the ideal condition. In the present study, the appropriateness of the real-time flow-rate estimation by decentralization of Kalman filters is verified by comparing it with two other types of existing real-time flow-rate estimations, i.e., time derivatives of the weight of the outflow liquid measured by the load cell and the liquid volume in the ladle measured by a visible camera. We especially confirmed the estimation errors of the candidate real-time flow-rate estimations in the experiments with the uncertainty of the model parameters. These flow-rate estimation methods were applied to a laboratory-type automatic pouring machine to verify their performance.

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 Mixture of Lindley and Inverse Weibull Distributions: Properties and Estimation

2021 ◽  
Vol 20 ◽  
pp. 134-143
Author(s):  
A. S. Al-Moisheer ◽  
A. F. Daghestani ◽  
K. S. Sultan
Keyword(s):  
Method Of Moments ◽  
Generalized Method Of Moments ◽  
Real Data ◽  
Estimation Methods ◽  
Simulation Studies ◽  
Weibull Distributions ◽  
Unknown Parameters ◽  
Data Application ◽  
Rate Functions ◽  
And Behavior

In this paper, we talk about a mixture of one-parameter Lindley and inverse Weibull distributions (MLIWD). First, We introduce and discuss the MLIWD. Then, we study the main statistical properties of the proposed mixture and provide some graphs of both the density and the associated hazard rate functions. After that, we estimate the unknown parameters of the proposed mixture via two estimation methods, namely, the generalized method of moments and maximum likelihood. In addition, we compare the estimation methods via some simulation studies to determine the efficacy of the two estimation methods. Finally, we evaluate the performance and behavior of the proposed mixture with different numerical examples and real data application in survival analysis.

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