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METHODS OF SURVIVAL ANALYSIS
Published in Richard G. Cornell, Statistical Methods for Cancer Studies, 2020
Dianne M. Finkelstein, Robert A. Wolfe
coincide with the Kaplan-Meier estimates. If there are no uncensored observations (only left and right censored), this estimate coincides with the Ayer tt a.¿. (1954) estimate of the empirical distribution function. The Ayer estimate maximizes the likelihood,
Prelude: Preliminary Tools and Foundations
Published in Albert Vexler, Alan D. Hutson, Statistics in the Health Sciences, 2018
We may note, for example, observing independent and identically distributed data points , one can estimate their distribution function via the empirical distribution function. Then the average , an estimator of , can be presented in the integral form using Lebesgue's integration.
High precision implementation of Steck's recursion method for use in goodness-of-fit tests
Published in Journal of Applied Statistics, 2022
Jiefei Wang, Jeffrey C. Miecznikowski
In a goodness of fit (GOF) scenario, the goal is to define how well a proposed statistical model describes a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the proposed model. For example, the well-known Kolmogorov–Smirnov statistic (see [9]) is based on the maximal distance between the empirical distribution function of the sample and cumulative distribution function (CDF) of the proposed distribution. The goodness of fit has application in regression models to assess normality of residuals and, ultimately, the validity of the standard assumptions for hypothesis testing of regression coefficients. GOF is also important in categorical data where chi-squared tests are used to evaluate assumptions about the data generating distribution. For example, in a random sample of 100 people, is it reasonable to assume men and women are equal in frequency?
A review of tests for exponentiality with Monte Carlo comparisons
Published in Journal of Applied Statistics, 2022
Everestus O. Ossai, Mbanefo S. Madukaife, Abimibola V. Oladugba
One distributional law that underlies a good number of statistical studies in life sciences, especially those that are related to renewal process, birth and death processes, Markov process, queuing theory and every other process characterized with appreciation and/or progressive decay, and reliability studies as well as survival analysis and generally in modeling is the exponential distribution. Goodness-of-fit test for exponentiality of a data set has been discussed extensively in the literature by a good number of authors. These include Gnedenko [51], Harris [54], Deshpande [37], Cox and Oakes [37], Epps and Pulley [41], Gail and Gastwirth [46], Baringhaus and Henze [23,24,25], Henze [58], Henze and Klar [59] and Abbasnejad et al. [1] to mention but a few. In fact, there exist dozens of different tests for assessing the exponentiality of data sets in the literature. The tests are based on certain characterizations of the exponential distribution such as empirical distribution function
Testing exponentiality based on the extropy of record values
Published in Journal of Applied Statistics, 2022
Peihan Xiong, Weiwei Zhuang, Guoxin Qiu
Tests based on entropy estimators.Tests based on correcting moments of entropy estimators.Tests based on Phi-divergence.Tests based on characterizations of the exponential distribution.Tests based on spacings.Tests based on Lorenz curve and Gini index.Tests based on the empirical distribution function.Tests based on the residual mean function.Tests based on the empirical Laplace transformation.Tests based on the empirical characteristic function.Tests based on correlation and covariance.Other tests.