### Journals Information

**
Mathematics and Statistics Vol. 9(5), pp. 736 - 743 DOI: 10.13189/ms.2021.090513 Reprint (PDF) (341Kb) **

## B-spline Estimation for Force of Mortality

**Tserenbat Oirov ^{1}, Gereltuya Terbish ^{2}^{,*}, Nyamsuren Dorj ^{2}**

^{1}Department of Applied Mathematics, National University of Mongolia, Mongolia

^{2}Department of Mathematics, Mongolian University Science and Technology, Mongolia

**ABSTRACT**

The paper focuses on the estimation of the force of mortality of living time distribution. We use a third-order B-spline function to construct the logarithm for force of mortality of living time. The number of the knots, their locations and B-spline coefficients based on a sample of observations are estimated by the maximum likelihood estimation method. Evaluation of B-spline parameters estimated by maximum likelihood estimation tested with criteria of the modified chi-squared goodness of the fit statistic. An algorithm developed to calculate Sequential Procedure for the modified chi-squared goodness of the fit testing. The Matlab code was written using the algorithm. Within this evaluation, the number of knots in the model has significantly reduced. The developed method was used to explain the mortality rate of women aged 0 to 69 among the Mongolian population in 2019 and estimate the life expectancy of Mongolians. The results of this experiment provided an excellent estimation of the force of mortality. Construction of a mortality rate estimation gives possibilities to determine mortality trends and force of mortality. Here, force of mortality is further used to construct a survival function, a lifetime distribution function, and a lifetime distribution probability density function. The method can also be used in financial market models and in models that estimate the useful life of equipment.

**KEYWORDS**

Maximum Likelihood Estimation, Force of Mortality, B-splines, Chi-square Statistic, Forecasting

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Tserenbat Oirov , Gereltuya Terbish , Nyamsuren Dorj , "B-spline Estimation for Force of Mortality," Mathematics and Statistics, Vol. 9, No. 5, pp. 736 - 743, 2021. DOI: 10.13189/ms.2021.090513.

(b). APA Format:

Tserenbat Oirov , Gereltuya Terbish , Nyamsuren Dorj (2021). B-spline Estimation for Force of Mortality. Mathematics and Statistics, 9(5), 736 - 743. DOI: 10.13189/ms.2021.090513.