Goodness-of-fit tests for the Gompertz distribution

Lénárt, Ádám; Missov, Trifon I.

doi:10.1080/03610926.2014.892323

Cited by 27 publications

(14 citation statements)

References 55 publications

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“…then (9) is the result (see, for example, Lenart and Missov 2015). The Gumbel distribution is a location-scale distribution with ν denoting the mode and β being the scale parameter.…”

Section: Application To Statistical Estimationmentioning

confidence: 99%

“…This dependency arises because of the truncation of the Gumbel distribution and because of the use of a instead of M as a parameter. Parameterization (3) partially overcomes this problem because it requires estimation of M instead of a (Lenart and Missov 2015). In mortality research, the "inverse relationship" between a and b is first identified by Strehler and Mildvan (1960, eq.…”

Section: Application To Statistical Estimationmentioning

confidence: 99%

See 1 more Smart Citation

The Gompertz force of mortality in terms of the modal age at death

Missov¹,

Lénárt²,

Németh³

et al. 2015

DemRes

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“…then (9) is the result (see, for example, Lenart and Missov 2015). The Gumbel distribution is a location-scale distribution with ν denoting the mode and β being the scale parameter.…”

Section: Application To Statistical Estimationmentioning

confidence: 99%

Section: Application To Statistical Estimationmentioning

confidence: 99%

The Gompertz force of mortality in terms of the modal age at death

Missov¹,

Lénárt²,

Németh³

et al. 2015

DemRes

Self Cite

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“…4. Entropy H measures heterogeneity in the age at death or, alternatively, the elasticity of life expectancy with respect to proportional changes in age-specific mortality (Keyfitz, 1977). It is defined as…”

Section: γGm Model-based Mortality Measuresmentioning

confidence: 99%

“…3. Life disparity e † measures, on the one hand, how much lifespans differ among individuals and, on the other hand, how many life years are lost because of death (Keyfitz, 1977). It is defined as the average remaining life expectancy at ages when deaths occur:…”

Section: γGm Model-based Mortality Measuresmentioning

confidence: 99%

How much can we trust life tables? Sensitivity of mortality measures to right-censoring treatment

2016

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International organizations, research institutions, insurance companies, pension funds and health policymakers calculate human mortality measures from life tables. Life-table data, though, are usually right-censored; that is, the last open-end age group does not contain information about the exact ages at death of individuals there, and mortality measures are sensitive to the way censoring is addressed. The standard way of "closing" the life table assumes a constant hazard of death for the last age group. This might lead to erroneous conclusions about mortality measures, especially when the open-end age interval contains a large proportion of the study population. In this article, we propose, instead, fitting a parametric model that well describes human mortality patterns, the gamma-GompertzMakeham, accounting for censoring, and constructing model-based equivalents of five mortality measures: life expectancy, the modal age at death, life disparity, entropy and the Gini coefficient. We show that, in comparison to conventional life-table measures, modelbased measures are less sensitive to the age at censoring or, equivalently, to the proportion of censored individuals, and can be only slightly distorted even if the age at censoring is low. This study also compares life-table and model-based mortality measures for a non-human population with an underlying Gompertz mortality schedule in which a fixed proportion of the population is censored. Using model-based mortality measures is essential when studying the mortality of populations subjected to substantial censoring; for instance, many life tables for developing countries contain an open-end interval that contains more than 10% of the population. In this study, we show that life expectancy at birth for Brazilian females in 2007, calculated by standard life-table algebra, exceeds by almost 3 years the gamma-GompertzMakeham model-based life expectancy. This article might serve as a basis for recalculation of mortality measures for all populations subjected to substantial censoring.

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“…On the one hand, the Gompertz distribution is a truncated (at 0) Gumbel distribution (see Gumbel 1958;Lenart and Missov 2014, for a broader discussion), which is a member of the class of generalized extreme value (GEV) distributions. The latter describe distributions of minima or maxima of a set of random variables.…”

Section: Gompertz-makeham Hazardmentioning

confidence: 99%