Do Suicides From the Golden Gate Bridge Cluster?

2016 ◽  
Vol 118 (1) ◽  
pp. 70-73
Author(s):  
Donald W. Mackenzie ◽  
David Lester ◽  
Russell Manson ◽  
Cynthia Yeh
Keyword(s):  
Poisson Process ◽  
Exponential Distribution ◽  
Null Hypothesis ◽  
Golden Gate ◽  
Negative Exponential Distribution ◽  
Anderson Darling ◽  
Clustering Data ◽  
Golden Gate Bridge ◽  
Negative Exponential ◽  
Over Time

Suicides from popular venues (known as “hotspots”) are often publicized and may result in imitation by subsequent suicides that may lead to clustering of the suicides over time. In order to examine whether the suicides from the Golden Gate Bridge showed clustering, data from the 224 suicides during 1999–2009 were analyzed using the Anderson-Darling Test was run on the data against a null hypothesis of a negative exponential distribution (as would be generated by a homogenous Poisson process). It was found that the data were almost a perfect fit for the Poisson distribution and so showed no evidence of clustering beyond that expected to occur by chance alone. This indicates that there was no imitation or contagion in the suicides from the Golden Gate Bridge.

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

2018 ◽  
pp. 439
Author(s):  
Hazim Mansour Gorgees ◽  
Bushra Abdualrasool Ali ◽  
Raghad Ibrahim Kathum
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Reliability Function ◽  
Bayes Estimator ◽  
Likelihood Estimator ◽  
Monte Carlo Simulation Technique ◽  
Negative Exponential Distribution ◽  
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

1965 ◽  
Vol 2 (02) ◽  
pp. 352-376 ◽  
Author(s):  
Samuel Karlin ◽  
James McGregor
Keyword(s):  
Exponential Distribution ◽  
Continuous Time ◽  
Random Variables ◽  
Independent Random Variables ◽  
Urn Models ◽  
Time Intervals ◽  
Negative Exponential Distribution ◽  
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).

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

1981 ◽  
Vol 18 (3) ◽  
pp. 652-659 ◽  
Author(s):  
M. J. Phillips
Keyword(s):  
Exponential Distribution ◽  
Random Variables ◽  
Reliability Theory ◽  
The Other ◽  
Independent Random Variables ◽  
System Availability ◽  
Failure Times ◽  
Negative Exponential Distribution ◽  
Negative Exponential

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

1980 ◽  
Vol 17 (04) ◽  
pp. 1117-1120 ◽  
Author(s):  
L. Valadares Tavares
Keyword(s):  
Exponential Distribution ◽  
Autocorrelation Function ◽  
Stationary Process ◽  
Autoregressive Process ◽  
Exact Distribution ◽  
Markovian Process ◽  
Negative Exponential Distribution ◽  
Negative Exponential

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

1981 ◽  
Vol 18 (03) ◽  
pp. 652-659 ◽  
Author(s):  
M. J. Phillips
Keyword(s):  
Exponential Distribution ◽  
Random Variables ◽  
Reliability Theory ◽  
The Other ◽  
Independent Random Variables ◽  
System Availability ◽  
Failure Times ◽  
Negative Exponential Distribution ◽  
Negative Exponential

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.

scholarly journals Sequential point and interval estimation of scale parameter of exponential distribution

1995 ◽  
Vol 18 (2) ◽  
pp. 383-390
Author(s):  
Z. Govindarajulu
Keyword(s):  
Exponential Distribution ◽  
Scale Parameter ◽  
Stopping Time ◽  
Interval Estimation ◽  
Location Parameter ◽  
Exact Expression ◽  
Point Estimation ◽  
Quadratic Loss ◽  
Negative Exponential Distribution ◽  
Negative Exponential

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

1970 ◽  
Vol 7 (2) ◽  
pp. 457-464 ◽  
Author(s):  
D. G. Tambouratzis
Keyword(s):  
Exponential Distribution ◽  
Present Note ◽  
Limiting Distribution ◽  
Loss System ◽  
Negative Exponential Distribution ◽  
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.

Suicides from the Golden Gate Bridge: Have They Changed over Time?

2010 ◽  
Vol 107 (2) ◽  
pp. 491-492 ◽  
Author(s):  
Cynthia Yeh ◽  
David Lester
Keyword(s):  
Golden Gate ◽  
Marin County ◽  
Golden Gate Bridge ◽  
Over Time

224 suicides from the Golden Gate Bridge in 1999–2009 were younger than other suicides handled by the Marin County Coroner but did not differ by sex or race. Those witnessed did not differ from those not witnessed. Compared to suicides from the bridge in the 1970s, recent suicides were older, more often male, and more often nonwhite.

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