Lognormal and log-logistic distribution mixture analysis and application

2021 ◽  
Author(s):  
Jelena Kočović ◽  
Vojislav V. Mitić ◽  
Marija Koprivica ◽  
Vesna Rajić ◽  
Goran Lazović
Keyword(s):  
Em Algorithm ◽  
Life Insurance ◽  
Expectation Maximization ◽  
Insurance Premium ◽  
Logistic Distribution ◽  
Mixture Analysis ◽  
Mortality Model ◽  
Premium Calculation ◽  
Distribution Mixture ◽  
Premium Rates

In this paper, we analyze a mixture of Lognormal and Log-Logistic distribution. We estimate the parameters of the introduced distribution by using the expectation-maximization (EM) algorithm. Various phenomena in the field of medicine and economy could be modeled by this mixture. In this paper, it is used to construct new mortality model for determining the unisex premium rates in life insurance. The application of the model is illustrated in the case of Serbian population and its advantages are presented in the context of life insurance premium calculation.

scholarly journals Estimating Crop Yield Insurance Premium Rates

1984 ◽  
Vol 13 (1) ◽  
pp. 119-127 ◽  
Author(s):  
Daniel J. Dudek ◽  
P. Geoffrey Allen
Keyword(s):  
Adverse Selection ◽  
Crop Yield ◽  
Technical Change ◽  
Calculation Method ◽  
Insurance Premium ◽  
Premium Calculation ◽  
Premium Rates ◽  
Insurance Rates ◽  
Definition Of ◽  
Yield Insurance

Insurance rates for crop yield protection programs have traditionally been calculated from county average yields. Where grower acreages and yields are not homogeneous, this approach leads to higher premiums and payouts and greater incidence of adverse selection. With individual grower data a production weighted rate premium calculation method can be used which avoids these problems. Furthermore, the definition of rate classes is not constrained to county boundaries. The additional complication of technical change is addressed and one solution is provided. Results are presented for the cranberry industry.

scholarly journals PERHITUNGAN PREMI ASURANSI JOINT LIFE DENGAN MODEL VASICEK DAN CIR

2019 ◽  
Vol 8 (3) ◽  
pp. 246
Author(s):  
I MADE WAHYU WIGUNA ◽  
KETUT JAYANEGARA ◽  
I NYOMAN WIDANA
Keyword(s):  
Stochastic Process ◽  
Interest Rates ◽  
Life Insurance ◽  
Insurance Premium ◽  
Insurance Contract ◽  
Insurance Company ◽  
Vasicek Model ◽  
Cir Model ◽  
Premium Payment ◽  
Premium Price

Premium is a sum of money that must be paid by insurance participants to insurance company, based on  insurance contract. Premium payment are affected by interest rates. The interest rates change according to stochastic process. The purpose of this work is to calculate the price of joint life insurance premiums with Vasicek and CIR models. The price of a joint life insurance premium with Vasicek and CIR models, at the age of the insured 35 and 30 years has increased until the last year of the contract. The price of a joint life insurance premium with Vasicek model is more expensive than the premium price using CIR model.

scholarly journals Unsupervised Learning in RSS-Based DFLT Using an EM Algorithm

Sensors ◽  
2021 ◽  
Vol 21 (16) ◽  
pp. 5549
Author(s):  
Ossi Kaltiokallio ◽  
Roland Hostettler ◽  
Hüseyin Yiğitler ◽  
Mikko Valkama
Keyword(s):  
Em Algorithm ◽  
Expectation Maximization ◽  
Tracking System ◽  
Model Parameters ◽  
Calibration Data ◽  
Tracking Accuracy ◽  
Time Period ◽  
The Em Algorithm ◽  
Device Free ◽  
Localization And Tracking

Received signal strength (RSS) changes of static wireless nodes can be used for device-free localization and tracking (DFLT). Most RSS-based DFLT systems require access to calibration data, either RSS measurements from a time period when the area was not occupied by people, or measurements while a person stands in known locations. Such calibration periods can be very expensive in terms of time and effort, making system deployment and maintenance challenging. This paper develops an Expectation-Maximization (EM) algorithm based on Gaussian smoothing for estimating the unknown RSS model parameters, liberating the system from supervised training and calibration periods. To fully use the EM algorithm’s potential, a novel localization-and-tracking system is presented to estimate a target’s arbitrary trajectory. To demonstrate the effectiveness of the proposed approach, it is shown that: (i) the system requires no calibration period; (ii) the EM algorithm improves the accuracy of existing DFLT methods; (iii) it is computationally very efficient; and (iv) the system outperforms a state-of-the-art adaptive DFLT system in terms of tracking accuracy.

scholarly journals PENERAPAN HUKUM MORTALITA MAKEHAM UNTUK PENENTUAN NILAI CADANGAN PREMI ASURANSI JOINT LIFE DENGAN METODE FACKLER

2020 ◽  
Vol 9 (3) ◽  
pp. 182
Author(s):  
MIFTAAHUL JANNAH ◽  
AGUS SUPRIATNA ◽  
RIAMAN RIAMAN
Keyword(s):  
Life Insurance ◽  
Insurance Companies ◽  
Estimated Parameters ◽  
Premium Calculation ◽  
Mortality Table

Joint life insurance is life insurance with an amount of more than one person, where the benefits are paid when one of the insured dies. The possibility of insurance companies will suffer losses if the claims that occur are more than predicted, so the premium reserve calculation is required. In this study, reserves were calculated using the Fackler method based on the Indonesian Mortality Table 2011 and the Makeham Assumption Mortality Table. The Indonesian Mortality Table 2011 was analyzed for the estimated parameters contained in the Makeham Assumption Mortality Table. Then the premium calculation and premium reserve calculation are done using the Fackler method based on the Makeham Assumption Mortality Table and the comparison uses the Indonesian Mortality Table 2011. The results of the calculation of the premiums based on the Makeham Assumption Mortality Table are greater than using the Indonesia Mortality Table 2011, while the premium reserve results are greater using the Indonesian Mortality Table 2011 than using the Makeham Assumption Mortality Table. This is because the chances of survival based on the Makeham Assumption Mortality Table are smaller than the Indonesian Mortality Table 2011.

scholarly journals Models and Algorithms for Tracking Target with Coordinated Turn Motion

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Xianghui Yuan ◽  
Feng Lian ◽  
Chongzhao Han
Keyword(s):  
Em Algorithm ◽  
Expectation Maximization ◽  
Multiple Models ◽  
Interacting Multiple Model ◽  
Multiple Model ◽  
Motion Model ◽  
Single Model ◽  
Kinematic Constraint ◽  
The Em Algorithm ◽  
Turn Rate

Tracking target with coordinated turn (CT) motion is highly dependent on the models and algorithms. First, the widely used models are compared in this paper—coordinated turn (CT) model with known turn rate, augmented coordinated turn (ACT) model with Cartesian velocity, ACT model with polar velocity, CT model using a kinematic constraint, and maneuver centered circular motion model. Then, in the single model tracking framework, the tracking algorithms for the last four models are compared and the suggestions on the choice of models for different practical target tracking problems are given. Finally, in the multiple models (MM) framework, the algorithm based on expectation maximization (EM) algorithm is derived, including both the batch form and the recursive form. Compared with the widely used interacting multiple model (IMM) algorithm, the EM algorithm shows its effectiveness.

scholarly journals MENENTUKAN FORMULA CADANGAN PREMI ASURANSI JIWA LAST SURVIVOR MENGGUNAKAN METODE NEW JERSEY

2019 ◽  
Vol 8 (4) ◽  
pp. 264
Author(s):  
I GUSTI AGUNG GEDE DWIPAYANA ◽  
I NYOMAN WIDANA ◽  
KARTIKA SARI
Keyword(s):  
New Jersey ◽  
Life Insurance ◽  
Insurance Premium ◽  
First Year ◽  
Premium Payment ◽  
Second Year ◽  
Annual Premium

Last survivor life insurance is a type of life insurance for two or more people, with premium payment up to the last death of the insured and at that time also provide the benefit from the insurer. The purpose of this research was to determine the formula for last survivor life insurance premium reserve using New Jersey method. To calculate the reserve: first we determine the benefit, and then the annuity and finnaly the annual premium. The premium reserve value in the New Jersey method on first year is zero. The premium reserve in the New Jersey method starts in the second year, for  years, with  where n represents the term of the insurance participant’s contract.

Note on Determination of Premium Rates for Motor Vehicles (Third Party Risks) Insurance in New Zealand

1972 ◽  
Vol 98 (2) ◽  
pp. 149-156
Author(s):  
J. E. Eriksen ◽  
E. J. Jones
Keyword(s):  
New Zealand ◽  
Life Insurance ◽  
Motor Vehicle ◽  
Third Party ◽  
Motor Vehicles ◽  
Motor Insurance ◽  
Premium Rates ◽  
Insurance Rates ◽  
Basic Ideas

The authors have advised on the level of motor vehicle (third party risks) insurance rates of premium in the circumstances under which that business is written in New Zealand and this paper records the approach taken. It has been prepared in the hope that, as no difficult mathematics are involved, the basic ideas may appeal both to actuaries and to persons other than actuaries who are interested in the transaction of non-life insurance. They are relevant not merely to third party motor insurance but also to non-life insurance generally in a situation where insurance is compulsory and the rates of premium are centrally controlled. In those circumstances more sophisticated techniques of deriving premium rates are less necessary.

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