scholarly journals The Transmuted Inverted Nadarajah-Haghighi Distribution With an Application to Lifetime Data

2021 ◽  
pp. 451-466
Author(s):  
Aliyeh Toumaj ◽  
S.M.T.K. MirMostafaee ◽  
G.G. Hamedani
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Interval Estimation ◽  
Likelihood Estimation ◽  
Lifetime Distribution ◽  
Lifetime Data ◽  
Unknown Parameters ◽  
Failure Data ◽  
Mathematical Properties ◽  
New Distribution

In this paper, we propose a new lifetime distribution. We discuss several mathematical properties of the new distribu- tion. Certain characterizations of the new distribution are provided. We study the maximum likelihood estimation and asymptotic interval estimation of the unknown parameters. A simulation study, as well as an application of the new distribution to failure data, are also presented. We end the paper with a number of remarks.

scholarly journals New class of Lindley distributions: properties and applications

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Duha Hamed ◽  
Ahmad Alzaghal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Data Sets ◽  
Lifetime Data ◽  
Unknown Parameters ◽  
Lindley Distribution ◽  
New Class

AbstractA new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

scholarly journals Transmuted Modified Inverse Rayleigh Distribution

2015 ◽  
Vol 44 (3) ◽  
pp. 17-29 ◽  
Author(s):  
Muhammad Shuaib Khan ◽  
Robert King
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Order Statistics ◽  
Generating Function ◽  
Likelihood Estimation ◽  
Moment Generating Function ◽  
Rayleigh Distribution ◽  
Mean Deviation ◽  
Lifetime Data ◽  
Mathematical Properties

We introduce the transmuted modified Inverse Rayleighdistribution by using quadratic rank transmutation map (QRTM), whichextends the modified Inverse Rayleigh distribution. A comprehensiveaccount of the mathematical properties of the transmuted modified InverseRayleigh distribution are discussed. We derive the quantile, moments,moment generating function, entropy, mean deviation, Bonferroni andLorenz curves, order statistics and maximum likelihood estimation Theusefulness of the new model is illustrated using real lifetime data.

scholarly journals A Study on Properties and Applications of a Lomax Gompertz-Makeham Distribution

2019 ◽  
pp. 1-27
Author(s):  
Innocent Boyle Eraikhuemen ◽  
Terna Godfrey Ieren ◽  
Tajan Mashingil Mabur ◽  
Mohammed Sa’ad ◽  
Samson Kuje ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Probability Distributions ◽  
Real Life ◽  
Likelihood Estimation ◽  
The Other ◽  
Unknown Parameters ◽  
Method Of Maximum Likelihood ◽  
Compound Model ◽  
New Distribution

The article presents an extension of the Gompertz-Makeham distribution using the Lomax generator of probability distributions. This generalization of the Gompertz-Makeham distribution provides a more skewed and flexible compound model called Lomax Gompertz-Makeham distribution. The paper derives and discusses some Mathematical and Statistical properties of the new distribution. The unknown parameters of the new model are estimated via the method of maximum likelihood estimation. In conclusion, the new distribution is applied to two real life datasets together with two other related models to check its flexibility or performance and the results indicate that the proposed extension is more flexible compared to the other two distributions considered in the paper based on the two datasets used.

scholarly journals On the Transmuted AdditiveWeibull Distribution

2016 ◽  
Vol 42 (2) ◽  
pp. 117-132 ◽  
Author(s):  
Ibrahim Elbatal ◽  
Gokarna Aryal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Random Number ◽  
Continuous Distribution ◽  
Random Number Generation ◽  
Likelihood Estimation ◽  
Unknown Parameters ◽  
Real World Data ◽  
New Distribution

In this article a continuous distribution, the so-called transmuted additive Weibull distribution, that extends the additive Weibull distribution and some other distributions is proposed and studied. We will use the quadratic rank transmutation map proposed by Shaw and Buckley (2009) in order to generate the transmuted additiveWeibull distribution. Various structural properties of the new distribution including explicit expressions for the moments, random number generation and order statistics are derived. Maximum likelihood estimation of the unknown parameters of the new model for completesample is also discussed. It will be shown that the analytical results are applicable to model real world data.

Transmuted Erlang-Truncated Exponential Distribution

2016 ◽  
Vol 31 (2) ◽  
Author(s):  
Idika E. Okorie ◽  
Anthony C. Akpanta ◽  
Johnson Ohakwe
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Hazard Rate ◽  
Likelihood Estimation ◽  
Rate Function ◽  
Lifetime Distribution ◽  
Hazard Rate Function ◽  
Method Of Maximum Likelihood ◽  
Two Parameter ◽  
New Distribution

AbstractThis article introduces a new lifetime distribution called the transmuted Erlang-truncated exponential (TETE) distribution. This new distribution generalizes the two parameter Erlang-truncated exponential (ETE) distribution. Closed form expressions for some of its distributional and reliability properties are provided. The method of maximum likelihood estimation was proposed for estimating the parameters of the TETE distribution. The hazard rate function of the TETE distribution can be constant, increasing or decreasing depending on the value of the transmutation parameter

FORWARD APPORTIONMENT OF CENSORED COUNTS FOR DISCRETE NONPARAMETRIC MAXIMUM LIKELIHOOD ESTIMATION OF FAILURE PROBABILITIES

2009 ◽  
Vol 16 (03) ◽  
pp. 213-234
Author(s):  
MINNIE H. PATEL ◽  
H.-S. JACOB TSAO
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Closed Form ◽  
Failure Probability ◽  
Likelihood Estimation ◽  
Lifetime Distribution ◽  
Nonparametric Maximum Likelihood ◽  
Kaplan Meier ◽  
Probability Estimates ◽  
Failure Probabilities

Empirical cumulative lifetime distribution function is often required for selecting lifetime distribution. When some test items are censored from testing before failure, this function needs to be estimated, often via the approach of discrete nonparametric maximum likelihood estimation (DN-MLE). In this approach, this empirical function is expressed as a discrete set of failure-probability estimates. Kaplan and Meier used this approach and obtained a product-limit estimate for the survivor function, in terms exclusively of the hazard probabilities, and the equivalent failure-probability estimates. They cleverly expressed the likelihood function as the product of terms each of which involves only one hazard probability ease of derivation, but the estimates for failure probabilities are complex functions of hazard probabilities. Because there are no closed-form expressions for the failure probabilities, the estimates have been calculated numerically. More importantly, it has been difficult to study the behavior of the failure probability estimates, e.g., the standard errors, particularly when the sample size is not very large. This paper first derives closed-form expressions for the failure probabilities. For the special case of no censoring, the DN-MLE estimates for the failure probabilities are in closed forms and have an obvious, intuitive interpretation. However, the Kaplan–Meier failure-probability estimates for cases involving censored data defy interpretation and intuition. This paper then develops a simple algorithm that not only produces these estimates but also provides a clear, intuitive justification for the estimates. We prove that the algorithm indeed produces the DN-MLE estimates and demonstrate numerically their equivalence to the Kaplan–Meier-based estimates. We also provide an alternative algorithm.

The Poisson Nadarajah–Haghighi Distribution: Properties and Applications to Lifetime Data

2019 ◽  
Vol 27 (01) ◽  
pp. 2050005
Author(s):  
Muhammad Mansoor ◽  
M. H. Tahir ◽  
Aymaan Alzaatreh ◽  
Gauss M. Cordeiro
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Survival Data ◽  
Maximum Likelihood Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Likelihood Method ◽  
Lifetime Data ◽  
Monte Carlo Simulation Study ◽  
Mathematical Properties

A new three-parameter compounded extended-exponential distribution “Poisson Nadarajah–Haghighi” is introduced and studied, which is quite flexible and can be used effectively in modeling survival data. It can have increasing, decreasing, upside-down bathtub and bathtub-shaped failure rate. A comprehensive account of the mathematical properties of the model is presented. We discuss maximum likelihood estimation for complete and censored data. The suitability of the maximum likelihood method to estimate its parameters is assessed by a Monte Carlo simulation study. Four empirical illustrations of the new model are presented to real data and the results are quite satisfactory.

An Additive NHPP-Based Reliability Model of Wireless Sensor Networks

2014 ◽  
Vol 602-605 ◽  
pp. 3206-3212
Author(s):  
Bo Zhao ◽  
Jian Feng Yang ◽  
Ming Zhao ◽  
Qi Li ◽  
Yan Liu
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Wireless Sensor ◽  
Reliability Model ◽  
Unknown Parameters ◽  
Failure Data ◽  
Better Than

As the Wireless Sensor Networks (WSNs) are widely implemented in various fields recent years, the quality of WSNs has been increasingly concerned. WSNs can usually be divided into sub-nets, which assumed to work or fail independently. Through the failure data of those sub-nets, the additive NHPP model for reliability evaluation is composed, and then the maximum likelihood estimation is applied to estimate the unknown parameters in the model. Finally, the simulation shows that the additive NHPP model is better than general NHPP model under certain circumstances.

Sparse Code Shrinkage: Denoising of Nongaussian Data by Maximum Likelihood Estimation

1999 ◽  
Vol 11 (7) ◽  
pp. 1739-1768 ◽  
Author(s):  
Aapo Hyvärinen
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Sparse Coding ◽  
Likelihood Estimation ◽  
Wavelet Representation ◽  
Mathematical Properties ◽  
Important Benefit ◽  
Redundancy Reduction ◽  
Natural Data ◽  
Wavelet Methods

Sparse coding is a method for finding a representation of data in which each of the components of the representation is only rarely significantly active. Such a representation is closely related to redundancy reduction and independent component analysis, and has some neurophysiological plausibility. In this article, we show how sparse coding can be used for denoising. Using maximum likelihood estimation of nongaussian variables corrupted by gaussian noise, we show how to apply a soft-thresholding (shrinkage) operator on the components of sparse coding so as to reduce noise. Our method is closely related to the method of wavelet shrinkage, but it has the important benefit over wavelet methods that the representation is determined solely by the statistical properties of the data. The wavelet representation, on the other hand, relies heavily on certain mathematical properties (like self-similarity) that may be only weakly related to the properties of natural data.

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