Closed-form expressions to Gompertz-Makeham life expectancies: a historical note
نویسندگان
چکیده
Results well known in the actuarial community about closed-form expressions to Gompertz and Gompertz-Makeham life expectancies for a person aged x are still being independently rediscovered this day. This note seeks acknowledge previous results expectancies, especially science field, hoping stimulate interdisciplinarity provide background further developments, since derivation of expectancy (and annuities) based on particular mortality laws matters interest multiple fields such as science, biology, demography, statistics among others.
منابع مشابه
The Gompertz-Makeham distribution
This work is about the Gompertz-Makeham distribution. The distribution has been applied plenty of times. The properties of the Gompertz-Makeham distribution investigated in this work are unimodality of the Gompertz-Makeham distribution and relationship between the median value and the mean residual life time of the Gompertz-Makeham distribution. For most of the realistic set of parameter values...
متن کاملClosed-Form Expressions for the Matrix Exponential
We discuss a method to obtain closed-form expressions of f(A), where f is an analytic function and A a square, diagonalizable matrix. The method exploits the Cayley–Hamilton theorem and has been previously reported using tools that are perhaps not sufficiently appealing to physicists. Here, we derive the results on which the method is based by using tools most commonly employed by physicists. W...
متن کاملClosed - form expressions for particle relative velocities induced by turbulence ( Research Note )
In this note we present complete, closed-form expressions for random relative velocities between colliding particles of arbitrary size in nebula turbulence. These results are exact for very small particles (those with stopping times much shorter than the large eddy overturn time) and are also surprisingly accurate in complete generality (that is, also apply for particles with stopping times com...
متن کاملStress-Strength and Ageing Intensity Analysis via a New Bivariate Negative Gompertz-Makeham Model
In Demography and modelling mortality (or failure) data the univariate Makeham-Gompertz is well-known for its extension of exponential distribution. Here, a bivariate class of Gompertz--Makeham distribution is constructed based on random number of extremal events. Some reliability properties such as ageing intensity, stress-strength based on competing risks are given. Also dependence properties...
متن کاملMalthus and Solow − a note on closed−form solutions
Recently, Jones (2002} and Barro and Sala−í−Martin (2004) pointed out that the neoclassical growth model with a Cobb−Douglas technology has a closed−form solution. This note makes a similar remark for the Malthusian model: I develop and characterize a closed−form solution. Moreover, I emphasize structural similarities between the Malthusian and the neoclassical model if the dynamic behavior is ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Revista Brasileira de Estudos de População
سال: 2022
ISSN: ['1980-5519', '0102-3098']
DOI: https://doi.org/10.20947/s0102-3098a0220