Consistent estimation of the density and hazard rate functions for censored data via the wavelet method

2005 ◽  
Vol 74 (4) ◽  
pp. 366-372 ◽  
Author(s):  
Paul H. Bezandry ◽  
George E. Bonney ◽  
Ali Gannoun
Keyword(s):  
Censored Data ◽  
Hazard Rate ◽  
Consistent Estimation ◽  
Wavelet Method ◽  
Rate Functions

scholarly journals Gamma Kernel Estimators for Density and Hazard Rate of Right-Censored Data

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
T. Bouezmarni ◽  
A. El Ghouch ◽  
M. Mesfioui
Keyword(s):  
Censored Data ◽  
Hazard Rate ◽  
Kernel Smoothing ◽  
Mean Squared Error ◽  
Boundary Region ◽  
Law Of Iterated Logarithm ◽  
Linear Estimator ◽  
Right Censored Data ◽  
Squared Error ◽  
Rate Functions

The nonparametric estimation for the density and hazard rate functions for right-censored data using the kernel smoothing techniques is considered. The “classical” fixed symmetric kernel type estimator of these functions performs well in the interior region, but it suffers from the problem of bias in the boundary region. Here, we propose new estimators based on the gamma kernels for the density and the hazard rate functions. The estimators are free of bias and achieve the optimal rate of convergence in terms of integrated mean squared error. The mean integrated squared error, the asymptotic normality, and the law of iterated logarithm are studied. A comparison of gamma estimators with the local linear estimator for the density function and with hazard rate estimator proposed by Müller and Wang (1994), which are free from boundary bias, is investigated by simulations.

Kumaraswamy odd Burr G family of distributions with applications to reliability data

2018 ◽  
Vol 55 (1) ◽  
pp. 94-114
Author(s):  
Arslan Nasir ◽  
Hassan S. Bakouch ◽  
Farrukh Jamal
Keyword(s):  
Asymptotic Behavior ◽  
Maximum Likelihood ◽  
Censored Data ◽  
Hazard Rate ◽  
Moment Generating Function ◽  
Density Functions ◽  
Censored Samples ◽  
The Family ◽  
Rate Functions ◽  
Family Of Distributions

We exhibit a general family of distributions named “Kumaraswamy odd Burr G family of distributions” with four additional parameters to generalize any existing baseline distribution. Some statistical properties of the family are derived, including rth moments, mth incomplete moments, moment generating function and entropies. The parameters of the family are estimated by the maximum likelihood (ML) method for complete sam- ples as well as censored samples. Some sub-models of the family are considered and it is noted that their density functions can be symmetric, left-skewed, right-skewed, unimodal, bimodal and their hazard rate functions can be increasing, decreasing, bathtub, upside- down bathtub and J-shaped. Simulation is carried out for one of the sub-models to check the asymptotic behavior of the ML estimates. Applications to reliability (complete and censored) data are carried out to check the usefulness of some sub-models of the family.

scholarly journals Comparison of multiple hazard rate functions

Biometrics ◽  
2015 ◽  
Vol 72 (1) ◽  
pp. 39-45 ◽  
Author(s):  
Zhongxue Chen ◽  
Hanwen Huang ◽  
Peihua Qiu
Keyword(s):  
Hazard Rate ◽  
Rate Functions

scholarly journals Transmuted Mukherjee-Islam Distribution: A Generalization of Mukherjee-Islam Distribution

2017 ◽  
Vol 9 (4) ◽  
pp. 135
Author(s):  
Loai M. A. Al-Zou'bi
Keyword(s):  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Continuous Distribution ◽  
Quantile Function ◽  
Descriptive Statistics ◽  
Likelihood Method ◽  
Distribution Parameters ◽  
Rate Functions ◽  
Mean Variance ◽  
New Distribution

A new continuous distribution is proposed in this paper. This distribution is a generalization of Mukherjee-Islam distribution using the quadratic rank transmutation map. It is called transmuted Mukherjee-Islam distribution (TMID). We have studied many properties of the new distribution: Reliability and hazard rate functions. The descriptive statistics: mean, variance, skewness, kurtosis are also studied. Maximum likelihood method is used to estimate the distribution parameters. Order statistics and Renyi and Tsallis entropies were also calculated. Furthermore, the quantile function and the median are calculated.

scholarly journals Characteristics of Hazard Rate Functions of Log-Normal Distributions

2019 ◽  
Vol 1338 ◽  
pp. 012036
Author(s):  
D Kurniasari ◽  
R Widyarini ◽  
Warsono ◽  
Y Antonio
Keyword(s):  
Hazard Rate ◽  
Normal Distributions ◽  
Rate Functions ◽  
Log Normal

Dynamic multivariate mean residual life functions

1991 ◽  
Vol 28 (03) ◽  
pp. 613-629 ◽  
Author(s):  
Moshe Shaked ◽  
J. George Shanthikumar
Keyword(s):  
Hazard Rate ◽  
Residual Life ◽  
Stochastic Ordering ◽  
Partial Ordering ◽  
Mean Residual Life ◽  
Positive Dependence ◽  
Basic Properties ◽  
Rate Functions ◽  
Hazard Rate Ordering ◽  
Weak Notion

In this paper we introduce and study a dynamic notion of mean residual life (mrl) functions in the context of multivariate reliability theory. Basic properties of these functions are derived and their relationship to the multivariate conditional hazard rate functions is studied. A partial ordering, called the mrl ordering, of non-negative random vectors is introduced and its basic properties are presented. Its relationship to stochastic ordering and to other related orderings (such as hazard rate ordering) is pointed out. Using this ordering it is possible to introduce a weak notion of positive dependence of random lifetimes. Some properties of this positive dependence notion are given. Finally, using the mrl ordering, a dynamic notion of multivariate DMRL (decreasing mean residual life) is introduced and studied. The relationship of this multivariate DMRL notion to other notions of dynamic multivariate aging is highlighted in this paper.

ON RELATIVE AGING COMPARISONS OF COHERENT SYSTEMS WITH IDENTICALLY DISTRIBUTED COMPONENTS

2020 ◽  
pp. 1-15 ◽  
Author(s):  
Nil Kamal Hazra ◽  
Neeraj Misra
Keyword(s):  
Hazard Rate ◽  
Sufficient Conditions ◽  
Stochastic Orders ◽  
Coherent System ◽  
Coherent Systems ◽  
Cumulative Hazard ◽  
Numerical Examples ◽  
Distributed Components ◽  
Rate Functions ◽  
Important Notion

The relative aging is an important notion which is useful to measure how a system ages relative to another one. Among the existing stochastic orders, there are two important orders describing the relative aging of two systems, namely, aging faster orders in the cumulative hazard and the cumulative reversed hazard rate functions. In this paper, we give some sufficient conditions under which one coherent system ages faster than another one with respect to the aforementioned stochastic orders. Further, we show that the proposed sufficient conditions are satisfied for k-out-of-n systems. Moreover, some numerical examples are given to illustrate the applications of proposed results.

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