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Fitting the Two‐Term Mixed Exponential and Two‐Parameter Lognormal Distributions to Grouped and Censored Data
Author(s) -
Marshall Malcomn L.
Publication year - 1974
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2347124
Subject(s) - log normal distribution , term (time) , statistics , mathematics , exponential function , exponential family , exponential distribution , econometrics , physics , mathematical analysis , quantum mechanics
Summary The paper considers several methods of fitting the two‐term mixed exponential and two‐parameter lognormal distributions to grouped and censored data. Of the methods considered, it is concluded that quantiles should be used to fit the mixed exponential distribution and unweighted least‐squares regression for the lognormal. The paper also considers the validity of testing the goodness‐of‐fit of the fitted distributions using a x 2 goodness‐of‐fit test. The paper concludes that the test statistic will be approximately x 2 distributed when fitting the lognormal distribution by regression to either of the two types of data considered (“cohort” and “census”). This will also be true for fitting a mixed exponential to census data but, when using this fitting method with cohort data, slightly more cases will be rejected by the x 2 ‐test than the significance level would suggest.