Estimation of parameters in Laplace distributions with interval censored data

. We derive maximum likelihood estimators for the parameters of the Laplace distribution for interval censored data. Existence and uniqueness of the estimators are proved. Simulations and real data applications show that the Laplace distribution can be a better model for interval censored data than competing models in spite of being simpler.

[1]  Arjun K. Gupta,et al.  Estimation Methods for the Gompertz–Makeham Distribution Under Progressively Type-I Interval Censoring Scheme , 2012 .

[2]  Pamela A Shaw,et al.  Exact and Asymptotic Weighted Logrank Tests for Interval Censored Data: The interval R package. , 2010, Journal of statistical software.

[3]  Chunyan Yang,et al.  Accelerated life test sampling plans for the Weibull distribution under Type I progressive interval censoring with random removals , 2010 .

[4]  Yuhlong Lio,et al.  Parameter estimations for generalized exponential distribution under progressive type-I interval censoring , 2010, Comput. Stat. Data Anal..

[5]  K. Gajjar,et al.  Inference under Progressive Interval Censoring for Geometric Distribution , 2010 .

[6]  Hon Keung Tony Ng,et al.  Statistical estimation for the parameters of Weibull distribution based on progressively type-I interval censored sample , 2009 .

[7]  Chunyan Yang,et al.  Optimal accelerated life tests under interval censoring with random removals: the case of Weibull failure distribution , 2008 .

[8]  D. Park.  The Statistical Analysis of Interval-Censored Failure Time Data , 2007 .

[9]  J. Mi,et al.  Estimation of parameters in logistic and log-logistic distribution with grouped data , 2007, Lifetime data analysis.

[10]  Naji Younes,et al.  Parametric survival models for interval-censored data with time-dependent covariates. , 2006, Biostatistics.

[11]  Gordon Johnston,et al.  Statistical Models and Methods for Lifetime Data , 2003, Technometrics.

[12]  S. Tse,et al.  Statistical Analysis of Exponential Lifetimes Under an Integrated Type-Ii Interval Censoring Scheme , 2002 .

[13]  Werner Hürlimann,et al.  Financial Data Analysis with Two Symmetric Distributions , 2001 .

[14]  J. Horowitz,et al.  Estimating the frequency of high microbial counts in commercial food products using various distribution functions. , 2001, Journal of food protection.

[15]  J. Lindsey,et al.  Generalized Nonlinear Models for Pharmacokinetic Data , 2000, Biometrics.

[16]  A. Scallan.  Regression modelling of interval-censored failure time data using the Weibull distribution , 1999 .

[17]  W. Cleveland.  LOWESS: A Program for Smoothing Scatterplots by Robust Locally Weighted Regression , 1981 .

[18]  W. Cleveland.  Robust Locally Weighted Regression and Smoothing Scatterplots , 1979 .

[19]  H. Akaike.  A new look at the statistical model identification , 1974 .

[20]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[21]  Tzong-Ru Tsai,et al.  Parameter Estimations for Generalized Rayleigh Distribution under Progressively Type-I Interval Censored Data , 2011 .

[22]  G. Rodŕıguez,et al.  Parametric Survival Models , 2010 .

[23]  Tzong-Ru Tsai,et al.  Interval censored sampling plans for the gamma lifetime model , 2009, Eur. J. Oper. Res..

[24]  Narayanaswamy Balakrishnan,et al.  Planning life tests with progressively Type-I interval censored data from the lognormal distribution , 2009 .

[25]  Zeinab H. Amin.  A note on the parameter estimation for the lognormal distribution based on progressively Type I interval censored samples , 2008, Model. Assist. Stat. Appl..

[26]  Saralees Nadarajah,et al.  Multitude of Laplace distributions , 2008 .

[27]  Krzysztof Podgórski,et al.  LOG-LAPLACE DISTRIBUTIONS , 2003 .

[28]  T. Kozubowski,et al.  A Log-Laplace growth rate model , 2003 .

[29]  M. Peleg.  Interpretation of the irregularly fluctuating microbial counts in commercial dairy products , 2002 .

[30]  J. K. Lindsey,et al.  A Study of Interval Censoring in Parametric Regression Models , 1998, Lifetime data analysis.

[31]  T. Ferguson.  A Course in Large Sample Theory , 1996 .

[32]  P. W. Lane.  Generalized Nonlinear Models , 1996 .

[33]  V. Uppuluri.  Some Properties of the Log-Laplace Distribution , 1981 .