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Understanding the shape of the mixture failure rate (with engineering and demographic applications)

Maxim Finkelstein
2009 Applied Stochastic Models in Business and Industry  
Therefore, the study of the shape of the observed (mixture) failure rate in a heterogeneous setting is important in many applications.  ...  We study discrete and continuous mixtures, obtain conditions for the mixture failure rate to tend to the failure rate of the strongest populations and describe asymptotic behavior as ∞ → t .  ...  Therefore the mixture model results in the dramatically different shape (the upside-down bathtub shape) when after a certain point the mixture failure rate is decreasing.  ... 
doi:10.1002/asmb.815 fatcat:s7ortdmdjvec5adaw47rot4ky4

Heterogeneity in multistage carcinogenesis and mixture modeling

Sandro Gsteiger, Stephan Morgenthaler
2008 Theoretical Biology and Medical Modelling  
In this article, we consider extensions of the multistage carcinogenesis model by mixture modeling. This approach allows us to describe population heterogeneity in a biologically meaningful way.  ...  We focus on finite mixture models, for which we prove identifiability. These models are applied to human lung cancer data from several birth cohorts.  ...  The first author has been supported by a grant from the Swiss National Science Foundation.  ... 
doi:10.1186/1742-4682-5-13 pmid:18644142 pmcid:PMC2515834 fatcat:hc5kmqhjzvelrf6si7sie24hie

A new class of distributions as a finite functional mixture using functional weights

DALAL LALA BOUALI, CHRISTOPHE CHESNEAU, VIKAS KUMAR SHARMA, HASSAN S. BAKOUCH
2021 Anais da Academia Brasileira de Ciências  
For estimating the parameters, the method of maximum likelihood estimation is used. Two applications with practical data sets are given.  ...  In this paper, we introduce a new family of distributions whose probability density function is defined as a weighted sum of two probability density functions; one is defined as a warped version of the  ...  Sharma greatly acknowledges the financial support from Science and Engineering Research Board, Department of Science & Technology, Govt. of India, under the scheme Early Career Research Award (file no.  ... 
doi:10.1590/0001-3765202120181019 pmid:34190839 fatcat:65eqnjq6hjamdptrvfotrmzggi

On ageing properties of lifetime distributions [article]

Anakha K K, V M Chacko
2021 arXiv   pre-print
A reasonable segment of reliability theory is perpetrated to the study of failure rates, their properties, connections and applications.  ...  The present study focused on failure rate distributions and their shape properties.  ...  Modified bathtub shaped failure rate (MBFR) if ( ) ht is first increasing and then bathtub shaped; 6.  ... 
arXiv:2107.09921v1 fatcat:sltrfypvfvbdvc4qwewh7m5gbm

DeepGMR: Learning Latent Gaussian Mixture Models for Registration [article]

Wentao Yuan, Ben Eckart, Kihwan Kim, Varun Jampani, Dieter Fox, Jan Kautz
2020 arXiv   pre-print
as the minimization of KL-divergence between two probability distributions modeled as mixtures of Gaussians.  ...  Point cloud registration is a fundamental problem in 3D computer vision, graphics and robotics.  ...  With the learned correspondence, a point can be associated to a distant component based on the context of the entire shape rather than a local neighborhood.  ... 
arXiv:2008.09088v1 fatcat:ry32yli54vg2roymviiw7ha3ry

Harmonic Mixture-G Family of Distributions: Survival Regression, Simulation by Likelihood, Bootstrap and Bayesian Discussion with MCMC Algorithm

Omid Kharazmi, Ali Saadati Nik, G.G. Hamedani, Emrah Altun
2022 Austrian Journal of Statistics  
To study the heterogeneous nature of lifetimes of certain mechanical or engineering processes, a mixture model of some suitable lifetime distributions may be more appropriate and appealing than simpler  ...  In this paper, a new mixture family of the lifetime distributions is introduced via harmonic weighted mean of an underlying distribution and the distribution of the proportional hazard model corresponding  ...  The concepts of increasing, decreasing, bathtub shaped (first decreasing and then increasing) and upside down bathtub shaped (first increasing and then decreasing) hazard rate functions are very useful  ... 
doi:10.17713/ajs.v51i2.1225 fatcat:zfuh5cnjunhm3nkcmg5wjdmkie

Econometric Analysis of Financial Trade Processes by Discrete Mixture Duration Models

Reinhard Hujer, Sandra Vuletic
2005 Social Science Research Network  
The Discrete Mixture ACD framework provides us with a general methodology which puts the idea into practice.  ...  It is established by introducing a discrete-valued latent regime variable which can be justified in the light of recent market microstructure theories.  ...  Contrary to this practice a mix of different distribution types seems to be reasonable which can be argued from a theoretical point of view.  ... 
doi:10.2139/ssrn.766664 fatcat:ugmrjln5l5bvzcnjerydbmipla

Econometric analysis of financial trade processes by discrete mixture duration models

Reinhard Hujer, Sandra Vuletić
2007 Journal of Economic Dynamics and Control  
The Discrete Mixture ACD framework provides us with a general methodology which puts the idea into practice.  ...  It is established by introducing a discrete-valued latent regime variable which can be justified in the light of recent market microstructure theories.  ...  Contrary to this practice a mix of different distribution types seems to be reasonable which can be argued from a theoretical point of view.  ... 
doi:10.1016/j.jedc.2005.09.015 fatcat:rhfrg32csfad7im7tocr6yeuxy

A New Flexible Bathtub-Shaped Modification of the Weibull Model: Properties and Applications

Qinghu Liao, Zubair Ahmad, Eisa Mahmoudi, G. G. Hamedani
2020 Mathematical Problems in Engineering  
For the illustrative purposes, two real applications from reliability engineering with bathtub-shaped hazard functions are analyzed.  ...  In this paper, we combine the logarithms of two cumulative hazard rate functions and propose a new modified form of the Weibull distribution.  ...  of the bathtub-shaped failure rate closely (see Figure 3 ). (6) It may provide a better fit to the reliability data having a bathtub-shaped failure rate function than the other well-known bathtub-shaped  ... 
doi:10.1155/2020/3206257 fatcat:jvlxdt34jzbfdhbaxno7zjjapu

Stochastically Ordered Subpopulations and Optimal Burn-In Procedure

Ji Hwan Cha, Maxim Finkelstein
2010 IEEE Transactions on Reliability  
In the studies of burn-in, the assumption of bathtub shaped failure rate function is usually employed and optimal burn-in procedures are investigated.  ...  Burn-in is a widely used engineering method which is adopted to eliminate defective items before they are shipped to customers or put into the field operation.  ...  The work of the second author was supported by the NRF (National Research Foundation of South Africa) grant FA2006040700002.  ... 
doi:10.1109/tr.2010.2055925 fatcat:ossgbceqpbcvpdsfrygh6egjuu

Mixture Modeling of Exponentiated Pareto Distribution in Bayesian Framework with Applications of Wind-speed and Tensile Strength of Carbon Fiber

Ammara Nawaz Cheema, Muhammad Aslam, Ibrahim M. Almanjahie, Ishfaq Ahmad
2020 IEEE Access  
The presentation of the Bayes estimator(s) over posterior risk(s) in the studied loss functions is examined over simulation practice.  ...  Bayesian demonstration of 3-Component mixture model of Exponentiated Pareto distribution in right-type-I censoring scheme is presented in this article.  ...  This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.  ... 
doi:10.1109/access.2020.3027369 fatcat:qtzrv7wu6beklpjk4fgu5abbla

Weibull Model Allowing Nearly Instantaneous Failures

C. D. Lai, Michael B. C. Khoo, K. Muralidharan, M. Xie
2007 Journal of Applied Mathematics and Decision Sciences  
A generalized Weibull model that allows instantaneous or early failures is modified so that the model can be expressed as a mixture of the uniform distribution and the Weibull distribution.  ...  Properties of the resulting distribution are derived; in particular, the probability density function, survival function, and the hazard rate function are obtained.  ...  Acknowledgments The first author is privileged to have been a former student and a colleague of Professor Jeff Hunter, who has been an inspiration to many.  ... 
doi:10.1155/2007/90842 fatcat:5me5uhl2lvajhnxceyi7kzknby

Weibull, κ-Weibull and other probability distributions

Amelia Carolina Sparavigna
2022 Zenodo  
As a consequence, the κ-Weibull function turns out to be quite relevant for generalizations of the Weibull approach to modeling failure times.  ...  The most important observation, coming from the proposed calculations, is that the κ-Weibull hazard function is strongly depending on the values of parameter κ, a parameter which is deeply influencing  ...  The name of the curve is derived from the cross-sectional shape of a bathtub, which has steep sides and a flat bottom. These items have hazard rate which is high initially and low in the centre.  ... 
doi:10.5281/zenodo.6425210 fatcat:xpo54fs35rfulejhmsg42thd7q

Interactions Between Ageing and Risk Properties in the Analysis of Burn-in Problems

Rachele Foschi, Fabio Spizzichino
2012 Decision Analysis  
In this paper, we in particular point out some aspects concerning interactions between the probabilistic model for lifetimes and considerations of an economic kind.  ...  However, in this frame, the so-called burn-in problem can be seen as a problem of risk-taking par excellence.  ...  Delquié for pointing out the interest of the reference Bordley and LiCalzi (2000) .  ... 
doi:10.1287/deca.1120.0236 fatcat:mxyssk3dojcolay5djbe7e54xm

Weibull, κ-Weibull and other probability distributions

Amelia Carolina Sparavigna
2022 Zenodo  
As a consequence, the κ-Weibull function turns out to be quite relevant for generalizations of the Weibull approach to modeling failure times.  ...  The most important observation, coming from the proposed calculations, is that the κ-Weibull hazard function is strongly depending on the values of parameter κ, a parameter which is deeply influencing  ...  The name of the curve is derived from the cross-sectional shape of a bathtub, which has steep sides and a flat bottom. These items have hazard rate which is high initially and low in the centre.  ... 
doi:10.5281/zenodo.6457168 fatcat:udbh3xo6e5evbntvhqhtbuiobm
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