Realisation of the mean-value function

1973 ◽  
Vol 9 (22) ◽  
pp. 528
Author(s):  
E. Ball
Keyword(s):  
Value Function ◽  
Mean Value ◽  
The Mean

A stochastic model for time lag in reporting of claims

1974 ◽  
Vol 11 (02) ◽  
pp. 382-387 ◽  
Author(s):  
Jan-Erik Karlsson
Keyword(s):  
Integral Equation ◽  
Stochastic Model ◽  
Renewal Process ◽  
Value Function ◽  
Time Lag ◽  
Mean Value ◽  
Time Interval ◽  
Asymptotic Expressions ◽  
The Laplace Transform ◽  
The Mean

We assume that the number of claims occur according to a renewal process and treat the number of claims that occur and are reported in a certain time interval as a renewal process with random displacements. We obtain a renewal equation for the mean value function and an integral equation for the Laplace transform of the distribution of the claims that are reported. We also give asymptotic expressions for the mean value function and calculate the generating function in the case where the renewal process is a Poisson process. This matter is a part of the IBNR-problem in insurance mathematics.

INTEGRATION OF IMPERFECT DEBUGGING IN GENERAL TESTING-DOMAIN DEPENDENT NHPP SRGM

2005 ◽  
Vol 12 (06) ◽  
pp. 493-505 ◽  
Author(s):  
JOONG-YANG PARK ◽  
YANG-SOOK HWANG ◽  
TAKAJI FUJIWARA
Keyword(s):  
Value Function ◽  
Reduction Rate ◽  
Mean Value ◽  
Value Functions ◽  
Testing Strategy ◽  
Imperfect Debugging ◽  
Empirical Performance ◽  
Rate Functions ◽  
The Mean ◽  
Constant Fault

Recently the general testing-domain dependent NHPP SRGM is developed to reflect repeated execution of constructs and location of detected faults. It assumes that debugging is perfect. Since realistic models need to reflect imperfect debugging, this paper integrates imperfect debugging in the general testing-domain dependent NHPP SRGM. Differential equations representing the mean value function are first derived for general testing strategy and then realized for the uniform testing. Specific mean value functions are obtained for some selected fault detection rate functions and constant fault reduction rate. Finally empirical performance evaluation is fulfilled.

An application of the minimum discrimination information estimate to compute log-likelihood ratios

1973 ◽  
Vol 10 (2) ◽  
pp. 469-474
Author(s):  
E. L. Melnick ◽  
S. Kullback
Keyword(s):  
Continuous Time ◽  
Value Function ◽  
Mean Value ◽  
The Other ◽  
Likelihood Ratios ◽  
Log Likelihood ◽  
Discrimination Information ◽  
The Mean ◽  
Nikodym Derivative ◽  
Minimum Discrimination Information

In this paper the minimum discrimination information estimate is used to compute the log-likelihood ratio or logarithm of the Radon-Nikodym derivative In (dP1/dP2) when the stochastic process {x(t), t∈T) has either the probability measure P1 or P2. One example tests the mean value function of Gaussian processes. The other tests the mean value function of a continuous time Poisson process.

Closure and Monotonicity Properties of Nonhomogeneous Poisson Processes and Record Values

1988 ◽  
Vol 2 (4) ◽  
pp. 475-484 ◽  
Author(s):  
Ramesh C. Gupta ◽  
S.N.U.A. Kirmani
Keyword(s):  
Value Function ◽  
Record Values ◽  
Mean Value ◽  
Poisson Processes ◽  
Minimal Repair ◽  
Nonhomogeneous Poisson Processes ◽  
Upper Record Values ◽  
The Mean ◽  
Upper Record ◽  
Occurrence Times

Interconnections between occurrence times of nonhomogeneous Poisson processes, record values, minimal repair times, and the relevation transform are explained. A number of properties of the distributions of occurrence times and interoccurrence times of a nonhomogeneous Poisson process are proved when the mean-value function of the process is convex, starshaped, or superadditive. The same results hold for upper record values of independently identically distributed random variables from IFR, IFRA, and NBU distributions.

A stochastic model for time lag in reporting of claims

1974 ◽  
Vol 11 (2) ◽  
pp. 382-387 ◽  
Author(s):  
Jan-Erik Karlsson
Keyword(s):  
Integral Equation ◽  
Stochastic Model ◽  
Renewal Process ◽  
Value Function ◽  
Time Lag ◽  
Mean Value ◽  
Time Interval ◽  
Asymptotic Expressions ◽  
The Laplace Transform ◽  
The Mean

We assume that the number of claims occur according to a renewal process and treat the number of claims that occur and are reported in a certain time interval as a renewal process with random displacements. We obtain a renewal equation for the mean value function and an integral equation for the Laplace transform of the distribution of the claims that are reported. We also give asymptotic expressions for the mean value function and calculate the generating function in the case where the renewal process is a Poisson process. This matter is a part of the IBNR-problem in insurance mathematics.

An application of the minimum discrimination information estimate to compute log-likelihood ratios

1973 ◽  
Vol 10 (02) ◽  
pp. 469-474
Author(s):  
E. L. Melnick ◽  
S. Kullback
Keyword(s):  
Continuous Time ◽  
Value Function ◽  
Mean Value ◽  
The Other ◽  
Likelihood Ratios ◽  
Log Likelihood ◽  
Discrimination Information ◽  
The Mean ◽  
Nikodym Derivative ◽  
Minimum Discrimination Information

In this paper the minimum discrimination information estimate is used to compute the log-likelihood ratio or logarithm of the Radon-Nikodym derivative In (dP 1/dP 2) when the stochastic process {x(t), t∈T) has either the probability measure P 1 or P 2. One example tests the mean value function of Gaussian processes. The other tests the mean value function of a continuous time Poisson process.

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