TY - JOUR
T1 - Construction of multiple decrement tables under generalized fractional age assumptions
AU - Lee, Hangsuck
AU - Ahn, Jae Youn
AU - Ko, Bangwon
N1 - Funding Information:
The work of Jae Youn Ahn was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government ( NRF-2017R1D1A1B03032318 ).
Publisher Copyright:
© 2018 Elsevier B.V.
PY - 2019/5
Y1 - 2019/5
N2 - In this paper, we intend to develop a consistent methodology for constructing multiple decrement tables under generalized fractional age assumptions. Assuming that decrements have a common distribution at fractional ages, we derive conversion formulas to split or merge given multiple decrement tables in order to obtain a new multiple decrement table of interest. The assumptions that we consider are quite general, with a wide range of fractional age assumptions including the uniform distribution of decrements or the constant forces of decrement. Our proposed approaches allow us to directly obtain multiple decrement tables without the need for the associated single rates of decrement. They will also enable us to avoid potential inconsistency under the uniform distribution assumptions or unnaturalness arising from the constant forces assumption. In addition, as they navigate through a larger window, they will deepen our understanding of the classical results under the uniform distribution assumptions. Although our methodology is based on a common distribution function assumption, knowing the specific form of the function is unnecessary, since our conversion formulas do not depend upon it. Finally, numerical examples are illustrated where we investigate the main factors of the errors induced by the discrepancy between the true and assumed distributions. The numerical result shows that the relative errors under our approaches are practically negligible for moderate ranges of multiple decrement probabilities.
AB - In this paper, we intend to develop a consistent methodology for constructing multiple decrement tables under generalized fractional age assumptions. Assuming that decrements have a common distribution at fractional ages, we derive conversion formulas to split or merge given multiple decrement tables in order to obtain a new multiple decrement table of interest. The assumptions that we consider are quite general, with a wide range of fractional age assumptions including the uniform distribution of decrements or the constant forces of decrement. Our proposed approaches allow us to directly obtain multiple decrement tables without the need for the associated single rates of decrement. They will also enable us to avoid potential inconsistency under the uniform distribution assumptions or unnaturalness arising from the constant forces assumption. In addition, as they navigate through a larger window, they will deepen our understanding of the classical results under the uniform distribution assumptions. Although our methodology is based on a common distribution function assumption, knowing the specific form of the function is unnecessary, since our conversion formulas do not depend upon it. Finally, numerical examples are illustrated where we investigate the main factors of the errors induced by the discrepancy between the true and assumed distributions. The numerical result shows that the relative errors under our approaches are practically negligible for moderate ranges of multiple decrement probabilities.
KW - Associated single rates of decrement
KW - Common distribution of decrements
KW - Multiple decrement probabilities
UR - http://www.scopus.com/inward/record.url?scp=85054826140&partnerID=8YFLogxK
U2 - 10.1016/j.csda.2018.09.004
DO - 10.1016/j.csda.2018.09.004
M3 - Article
AN - SCOPUS:85054826140
SN - 0167-9473
VL - 133
SP - 104
EP - 119
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
ER -