Statistical Behaviour of Time Occurrences and Magnitude of Aftershock Sequences

Hazard Analysis ◽

Temporal Behaviour ◽

Aftershock Sequences ◽

Acceptable Model ◽

Negative Exponential ◽

R Relation

The negative exponential distribution of the magnitude (that is the well-known Gutenberg-Richter relation) and the negative exponential distribution of interarrival times constitute the backbone of the seismic hazard analysis.Our goal is to check if these two distributions could be considered an acceptable model also for aftershock sequences.We analysed several aftershock sequences, with mainshocks ranging from M=5.45&#160; to M=7.3; six sequences of Californian earthquakes selected from the SCEC database and an Italian sequence, selected from INGV-CNT Catalog.The results show that the G-R relation fits remarkably the data, with a &#946; value ranging from -1.8&#160; to -2.4. The temporal behaviour shows an acceptable fit to the negative exponential distribution:&#160; all the sequences exhibit a good fit for &#916;t>2.5 hours, on the contrary for &#916;t<2.5 hours Weibull distribution is more suitable.

The Comparison Between the Bayes Estimator and the Maximum Likelihood Estimator of the Reliability Function for Negative Exponential Distribution

Ibn AL- Haitham Journal For Pure and Applied Science ◽

10.30526/2017.ihsciconf.1815 ◽

2018 ◽

pp. 439

Author(s):

Hazim Mansour Gorgees ◽

Bushra Abdualrasool Ali ◽

Raghad Ibrahim Kathum

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimator ◽

Reliability Function ◽

Bayes Estimator ◽

Likelihood Estimator ◽

Monte Carlo Simulation Technique ◽

Negative Exponential ◽

Better Than

In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

Ehrenfest urn models

10.1017/s0021900200108708 ◽

1965 ◽

Vol 2 (02) ◽

pp. 352-376 ◽

Cited By ~ 25

Author(s):

Samuel Karlin ◽

James McGregor

Keyword(s):

Continuous Time ◽

Random Variables ◽

Independent Random Variables ◽

Urn Models ◽

Time Intervals ◽

Negative Exponential ◽

Random Times

In the Ehrenfest model with continuous time one considers two urns and N balls distributed in the urns. The system is said to be in stateiif there areiballs in urn I, N −iballs in urn II. Events occur at random times and the time intervals T between successive events are independent random variables all with the same negative exponential distributionWhen an event occurs a ball is chosen at random (each of theNballs has probability 1/Nto be chosen), removed from its urn, and then placed in urn I with probabilityp, in urn II with probabilityq= 1 −p, (0 <p< 1).

Waiting times, negative exponential distribution and generalized Fibonacci numbers

International Journal of Mathematical Education in Science and Technology ◽

10.1080/0020739800110209 ◽

1980 ◽

Vol 11 (2) ◽

pp. 197-200

Author(s):

G. V. Kass†

Keyword(s):

Waiting Times ◽

Fibonacci Numbers ◽

Generalized Fibonacci Numbers ◽

A characterization of the negative exponential distribution with application to reliability theory

10.2307/3213319 ◽

1981 ◽

Vol 18 (3) ◽

pp. 652-659 ◽

Cited By ~ 2

Author(s):

M. J. Phillips

Keyword(s):

Random Variables ◽

Reliability Theory ◽

The Other ◽

Independent Random Variables ◽

System Availability ◽

Failure Times ◽

The negative exponential distribution is characterized in terms of two independent random variables. Only one of the random variables has a negative exponential distribution whilst the other can belong to a wide class of distributions. This result is then applied to two models for the reliability of a system of two modules subject to revealed and unrevealed faults to show when the models are equivalent. It is also shown, under certain conditions, that the system availability is only independent of the distribution of revealed failure times in one module when unrevealed failure times in the other module have a negative exponential distribution.

An exponential Markovian stationary process

10.1017/s0021900200097436 ◽

1980 ◽

Vol 17 (04) ◽

pp. 1117-1120 ◽

Cited By ~ 8

Author(s):

L. Valadares Tavares

Keyword(s):

Autocorrelation Function ◽

Stationary Process ◽

Autoregressive Process ◽

Exact Distribution ◽

Markovian Process ◽

A new markovian process {X i : i = 0, 1, 2, ·· ·} following a negative exponential distribution and with the same autocorrelation function as the lag-1 autoregressive process is proposed and studied in this paper. The exact distribution of the maxima and of the minima of n consecutive Xi values are obtained and the exact expected upcrossing interval is given for any crossing level.

A characterization of the negative exponential distribution with application to reliability theory

10.1017/s0021900200098442 ◽

1981 ◽

Vol 18 (03) ◽

pp. 652-659 ◽

Cited By ~ 2

Author(s):

M. J. Phillips

Keyword(s):

Random Variables ◽

Reliability Theory ◽

The Other ◽

Independent Random Variables ◽

System Availability ◽

Failure Times ◽

Multi-stage procedures for the minimum risk and bounded risk point estimation of the location of negative exponential distribution under the modified LINEX loss function

Sequential Analysis ◽

10.1080/07474946.2019.1574444 ◽

2019 ◽

Vol 38 (2) ◽

pp. 135-162 ◽

Cited By ~ 1

Author(s):

Ajit Chaturvedi ◽

Sudeep R. Bapat ◽

Neeraj Joshi

Keyword(s):

Loss Function ◽

Point Estimation ◽

Linex Loss Function ◽

Minimum Risk ◽

Multi Stage ◽

Linex Loss ◽

Bounded Risk ◽

Sequential point and interval estimation of scale parameter of exponential distribution

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171295000470 ◽

1995 ◽

Vol 18 (2) ◽

pp. 383-390

Author(s):

Z. Govindarajulu

Keyword(s):

Scale Parameter ◽

Stopping Time ◽

Interval Estimation ◽

Location Parameter ◽

Exact Expression ◽

Point Estimation ◽

Quadratic Loss ◽

Sequential fixed-width confidence intervals are obtained for the scale parameterσwhen the location parameterθof the negative exponential distribution is unknown. Exact expressions for the stopping time and the confidence coefficient associated with the sequential fixed-width interval are derived. Also derived is the exact expression for the stopping time of sequential point estimation with quadratic loss and linear cost. These are numerically evaluated for certain nominal confidence coefficients, widths of the interval and cost functions, and are compared with the second order asymptotic expressions.

A note on Belyaev's limiting distribution of the intervals between losses in an n-server system

10.2307/3211982 ◽

1970 ◽

Vol 7 (2) ◽

pp. 457-464 ◽

Cited By ~ 1

Author(s):

D. G. Tambouratzis

Keyword(s):

Present Note ◽

Limiting Distribution ◽

Loss System ◽

Service Times ◽

Negative Exponential ◽

Server System

SummaryThe aim of the present note is to give an alternative simpler proof to a result of Belyaev [1], namely that in a loss system of n servers with recurrent input and negative exponential service times the intervals between losses, suitably scaled to have constant mean, tend to a negative exponential distribution as n tends to infinity.