Some tests for a poisson process and their powers with respect to trend in the intensity

Jani, P. N.; Shanubhogue, Ashok; Muralidharan, K.

doi:10.1080/03610929708832071

Cited by 3 publications

(3 citation statements)

References 6 publications

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“…Bain and Engelhardt [10], Jani et al [11] and Muralidharan [12] also proposed tests for HPP against PLP. By putting "1 in (7) we get the test statistic for an HPP as with mean and variance as Speci"cally, if we want to test H : ( "1, "1) vs H ( O1, "1), then the test procedure is to reject H for large values of Q* .…”

Section: Test Formentioning

confidence: 98%

“…Here, if the null hypothesis is true, that is when "1 and "1, then the times between failures are iid exponential random variables, and the process reduces to the homogeneous Poisson process. Bain and Engelhardt [10], Jani et al [11] and Muralidharan [12] also proposed tests for HPP against PLP. By putting "1 in (7) we get the test statistic for an HPP as Speci"cally, if we want to test H : ( "1, "1) vs H ( O1, "1), then the test procedure is to reject H for large values of Q* .…”

Section: Test For Hmentioning

confidence: 99%

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On testing of parameters in modulated power law process

Muralidharan

2001

Appl Stoch Models Bus & Ind

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SUMMARYThe modulated power law process (MPLP) is often used to model failure data from repairable system, when both renewal type behaviour and time trends are present. The MPLP allows for the failure rate of a system to be a!ected by the failure and repair. Since the MLEs of the estimates do not have closed form expressions, they have to be approximated, and hence deriving a test procedure will be di$cult. Black and Rigdon (1996) have proposed asymptotic MLEs and asymptotic likelihood ratio tests for the parameters which also do not have closed form expressions and hence are not easy for application. In this paper, we derive a closed form expression for the test statistics which is simple and easy to apply for testing (i) H : "1 versus H : O1 when is known and (ii) H : ( "1 and "1) versus H : ( O1 or O1). The simulation study for percentiles and powers are given. We also compare the performance of the test with that of Black and Rigdon's (1996) test. Some numerical examples are also provided to illustrate the testing procedures.

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Section: Test Formentioning

confidence: 98%

Section: Test For Hmentioning

confidence: 99%

On testing of parameters in modulated power law process

Muralidharan

2001

Appl Stoch Models Bus & Ind

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“…A detailed review of this process are given in Rigdon and Basu [24,25]. Baker [5], Jani et al [14] and Muralidharan [17] have proposed various tests for Weibull process. Recently Muralidharan [19] has studied reliability inferences of Weibull process under different realizations.…”

Section: ____________________________________________________________mentioning

confidence: 99%

Future Reliability Estimation Based on Predictive Distribution in Power Law Process

Muralidharan

Shah

Dhandhukia

2008

Quality Technology & Quantitative Management

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Power law process or Weibull process is used to model reliability growth. The reliability development of such a system often takes place by testing a system until it fails, then making repairs and design changes and testing it again. This process continues until a desired level of reliability is achieved. At various times in the development process it becomes important to assess and predict system reliability from an available set of data on system failures. We made an attempt to estimate the future reliability based on a predictive distribution. We also discuss the point and interval estimations of the parameters as well as reliability based on full likelihood and predictive likelihood. A detailed simulation along with a few examples is presented to support the developments.

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Modelling of Indian Stock Prices using Nonhomogeneous Poisson Processes with Time Trends

Shah¹

2013

IOSR-JBM

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Some tests for a poisson process and their powers with respect to trend in the intensity

Cited by 3 publications

References 6 publications

On testing of parameters in modulated power law process

On testing of parameters in modulated power law process

Future Reliability Estimation Based on Predictive Distribution in Power Law Process

Modelling of Indian Stock Prices using Nonhomogeneous Poisson Processes with Time Trends

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