scholarly journals A New Lifetime Distribution: Properties, Copulas, Applications, and Different Classical Estimation Methods

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Naif Alotaibi
Keyword(s):  
Least Square ◽  
Estimation Methods ◽  
Mean Deviation ◽  
Mean Residual Life ◽  
Least Square Estimation ◽  
New Model ◽  
Inactivity Time ◽  
Mean Inactivity Time ◽  
The Mean ◽  
Anderson Darling

A new continuous version of the inverse flexible Weibull model is proposed and studied. Some of its properties such as quantile function, moments and generating functions, incomplete moments, mean deviation, Lorenz and Bonferroni curves, the mean residual life function, the mean inactivity time, and the strong mean inactivity time are derived. The failure rate of the new model can be “increasing-constant,” “bathtub-constant,” “bathtub,” “constant,” “J-HRF,” “upside down bathtub,” “increasing,” “upside down-increasing-constant,” and “upside down.” Different copulas are used for deriving many bivariate and multivariate type extensions. Different non-Bayesian well-known estimation methods under uncensored scheme are considered and discussed such as the maximum likelihood estimation, Anderson Darling estimation, ordinary least square estimation, Cramér-von-Mises estimation, weighted least square estimation, and right tail Anderson Darling estimation methods. Simulation studies are performed for comparing these estimation methods. Finally, two real datasets are analyzed to illustrate the importance of the new model.

scholarly journals Expanded Fréchet Model: Mathematical Properties, Copula, Different Estimation Methods, Applications and Validation Testing

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1949
Author(s):  
Mukhtar M. Salah ◽  
M. El-Morshedy ◽  
M. S. Eliwa ◽  
Haitham M. Yousof
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Estimation Method ◽  
Least Square ◽  
Estimation Methods ◽  
Goodness Of Fit Test ◽  
Least Square Estimation ◽  
Chi Square ◽  
Anderson Darling ◽  
The Right

The extreme value theory is expanded by proposing and studying a new version of the Fréchet model. Some new bivariate type extensions using Farlie–Gumbel–Morgenstern copula, modified Farlie–Gumbel–Morgenstern copula, Clayton copula, and Renyi’s entropy copula are derived. After a quick study for its properties, different non-Bayesian estimation methods under uncensored schemes are considered, such as the maximum likelihood estimation method, Anderson–Darling estimation method, ordinary least square estimation method, Cramér–von-Mises estimation method, weighted least square estimation method, left-tail Anderson–Darling estimation method, and right-tail Anderson–Darling estimation method. Numerical simulations were performed for comparing the estimation methods using different sample sizes for three different combinations of parameters. The Barzilai–Borwein algorithm was employed via a simulation study. Three applications were presented for measuring the flexibility and the importance of the new model for comparing the competitive distributions under the uncensored scheme. Using the approach of the Bagdonavicius–Nikulin goodness-of-fit test for validation under the right censored data, we propose a modified chi-square goodness-of-fit test for the new model. The modified goodness-of-fit statistic test was applied for the right censored real data set, called leukemia free-survival times for autologous transplants. Based on the maximum likelihood estimators on initial data, the modified goodness-of-fit test recovered the loss in information while the grouping data and followed chi-square distributions. All elements of the modified goodness-of-fit criteria tests are explicitly derived and given.

scholarly journals Application to Engineering and Medical Data Using Three-Parameter Exponential Model

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Waleed Almutiry ◽  
Amani Abdullah Alahmadi ◽  
Ibrahim Elbatal ◽  
Ibrahim E. Ragab ◽  
Oluwafemi Samson Balogun ◽  
...  
Keyword(s):  
Simulation Analysis ◽  
Residual Life ◽  
Quantile Function ◽  
Exponential Model ◽  
Statistical Characteristics ◽  
Mean Residual Life ◽  
New Model ◽  
Conditional Moments ◽  
Mean Inactivity Time ◽  
Real World Datasets

This paper is devoted to a new lifetime distribution having three parameters by compound the exponential model and the transmuted Topp-Leone-G. The new proposed model is called the transmuted Topp-Leone exponential model; it is useful in lifetime data and reliability. The new model is very flexible; its pdf can be right skewness, unimodal, and decreasing shaped, but the hrf of the suggested model can be unimodal, constant, and decreasing. Numerous statistical characteristics of the new model, notably the quantile function, moments, incomplete moments, conditional moments, mean residual life, mean inactivity time, and entropy are produced and investigated. The system’s parameters are estimated using the maximum likelihood approach. All estimators should be theoretically convergent, which is supported by a simulation analysis. Finally, two real-world datasets from the engineering and medical disciplines explore the new model’s relevance and adaptability in comparison to the alternatives models such as the beta exponential, the Marshall–Olkin generalized exponential, the exponentiated Weibull, the modified Weibull, and the transmuted Burr type X models.

CHARACTERIZATIONS OF THE RHR AND MIT ORDERINGS AND THE DRHR AND IMIT CLASSES OF LIFE DISTRIBUTIONS

2005 ◽  
Vol 19 (4) ◽  
pp. 447-461 ◽  
Author(s):  
I. A. Ahmad ◽  
M. Kayid
Keyword(s):  
Hazard Rate ◽  
Stochastic Comparison ◽  
Hazard Rate Order ◽  
Reversed Hazard Rate ◽  
Inactivity Time ◽  
Time Order ◽  
Mean Inactivity Time ◽  
Life Distributions ◽  
The Mean ◽  
Decreasing Reversed Hazard Rate

Two well-known orders that have been introduced and studied in reliability theory are defined via stochastic comparison of inactivity time: the reversed hazard rate order and the mean inactivity time order. In this article, some characterization results of those orders are given. We prove that, under suitable conditions, the reversed hazard rate order is equivalent to the mean inactivity time order. We also provide new characterizations of the decreasing reversed hazard rate (increasing mean inactivity time) classes based on variability orderings of the inactivity time of k-out-of-n system given that the time of the (n − k + 1)st failure occurs at or sometimes before time t ≥ 0. Similar conclusions based on the inactivity time of the component that fails first are presented as well. Finally, some useful inequalities and relations for weighted distributions related to reversed hazard rate (mean inactivity time) functions are obtained.

SOME RESULTS ABOUT MIT ORDER AND IMIT CLASS OF LIFE DISTRIBUTIONS

2006 ◽  
Vol 20 (3) ◽  
pp. 481-496 ◽  
Author(s):  
Xiaohu Li ◽  
Maochao Xu
Keyword(s):  
Renewal Process ◽  
Residual Life ◽  
Random Time ◽  
Mean Residual Life ◽  
Stochastic Comparisons ◽  
Inactivity Time ◽  
Mean Inactivity Time ◽  
Life Distributions ◽  
Preservation Property

We investigate some new properties of mean inactivity time (MIT) order and increasing MIT (IMIT) class of life distributions. The preservation property of MIT order under increasing and concave transformations, reversed preservation properties of MIT order, and IMIT class of life distributions under the taking of maximum are developed. Based on the residual life at a random time and the excess lifetime in a renewal process, stochastic comparisons of both IMIT and decreasing mean residual life distributions are conducted as well.

Testing Behavior of the Mean Inactivity Time

2018 ◽  
Vol 46 (6) ◽  
pp. 20160611
Author(s):  
M. Kayid ◽  
S. Izadkhah
Keyword(s):  
Inactivity Time ◽  
Mean Inactivity Time ◽  
The Mean

scholarly journals A Novel Robust Model Predictive Controller for Aerospace Three-Phase PWM Rectifiers

Energies ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 2490 ◽  
Author(s):  
Tao Lei ◽  
Weiwei Tan ◽  
Guangsi Chen ◽  
Delin Kong
Keyword(s):  
Power System ◽  
Bayesian Estimation ◽  
Estimation Method ◽  
Parameters Estimation ◽  
Least Square ◽  
Estimation Methods ◽  
Control Performance ◽  
Least Square Estimation ◽  
Three Phase ◽  
Pwm Rectifiers

This paper presents a novel Model Predictive Direct Power Control (MPDPC) approach for the pulse width modulation (PWM) rectifiers in the Aircraft Alternating Current Variable Frequency (ACVF) power system. The control performance of rectifiers may be largely affected by variations in the AC side impedance, especially for systems with limited power volume system. A novel idea for estimating the impedance variation based on the Bayesian estimation, using an algorithm embedded in MPDPC is presented in this paper. The input filter inductance and its equivalent series resistance (ESR) of PWM rectifiers are estimated in this algorithm by measuring the input current and input voltage in each cycle with the probability Bayesian estimation theory. This novel estimation method can overcome the shortcomings of traditional data based estimation methods such as least square estimation (LSE), which achieves poor estimation results with the small samples data set. In ACVF systems, the effect on the parameters estimation accuracy caused by the number of sampling points in one cycle is also analyzed in detail by simulation. The validity of this method is verified by the digital and Hard-in-loop simulation compared with other estimation methods such as the least square estimation method. The experimental testing results show that the proposed estimation algorithm can improve the robustness and the control performance of the MPDPC under the condition of the uncertainty of the AC side parameters of the three-phase PWM rectifiers in aircraft electrical power system.

FURTHER RESULTS INVOLVING THE MIT ORDER AND THE IMIT CLASS

2005 ◽  
Vol 19 (3) ◽  
pp. 377-395 ◽  
Author(s):  
I. A. Ahmad ◽  
M. Kayid ◽  
F. Pellerey
Keyword(s):  
Reliability Theory ◽  
Convex Order ◽  
Lifetime Distributions ◽  
Increasing Convex Order ◽  
Shock Models ◽  
Inactivity Time ◽  
Mean Inactivity Time ◽  
Time Class ◽  
Right Spread Order ◽  
The Mean

The purpose of this article is to study several preservation properties of the mean inactivity time order under the reliability operations of convolution, mixture, and shock models. In that context, the increasing mean inactivity time class of lifetime distributions is characterized by means of right spread order and increasing convex order. Some applications in reliability theory are described. Finally, a new test of such a class is discussed.

scholarly journals Estimation of density and distribution functions of a Burr X distribution

2018 ◽  
Vol 52 (1) ◽  
pp. 43-59
Author(s):  
AMULYA KUMAR MAHTO ◽  
YOGESH MANI TRIPATH ◽  
SANKU DEY
Keyword(s):  
Mean Squared Error ◽  
Real Data ◽  
Distribution Functions ◽  
Least Square ◽  
Efficient Estimation ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Unbiased Estimation ◽  
Least Square Estimation ◽  
Data Set

Burr type X distribution is one of the members of the Burr family which was originally derived by Burr (1942) and can be used quite effectively in modelling strength data and also general lifetime data. In this article, we consider efficient estimation of the probability density function (PDF) and cumulative distribution function (CDF) of Burr X distribution. Eight different estimation methods namely maximum likelihood estimation, uniformly minimum variance unbiased estimation, least square estimation, weighted least square estimation, percentile estimation, maximum product estimation, Cremer-von-Mises estimation and Anderson-Darling estimation are considered. Analytic expressions for bias and mean squared error are derived. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Finally, a real data set has been analyzed for illustrative purposes.

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