The Missing Tail and Other Considerations for the Use of Fire History Models

1995 ◽  
Vol 5 (4) ◽  
pp. 197 ◽  
Author(s):  
MA Finney
Keyword(s):  
Exponential Distribution ◽  
Exponential Model ◽  
Forest Age ◽  
Age Classes ◽  
Class Distribution ◽  
Age Class ◽  
Negative Exponential Distribution ◽  
Negative Exponential Model ◽  
Negative Exponential ◽  
Tests Of Fit

This paper reviews methods used for testing the fit of the cumulative form of a negative exponential distribution to the cumulative distribution of forest age-classes. It is shown that existing methods can lead to a greater chance of falsely rejecting the fit of the negative exponential model and inferring that fire frequencies have changed through time. This results when the old-age tail of a negative exponential distribution is mathematically assumed to be present at the end of the age-class distribution. In reality, the tail is censored from sample distributions of forest age-classes. Censoring alters the shape of a cumulative age-class distribution from the straight line expected for a semi-log graph of the cumulative negative exponential model. A solution to this problem is proposed that restricts the tests-of-fit to the portion of the negative exponential distribution that overlaps with the data to be tested. The cumulative age-class distribution can then be compared directly with the cumulative of a truncated negative exponential distribution. Considerations for interpreting a poor fit are then discussed.

Age-class distribution and the forest fire cycle

1978 ◽  
Vol 8 (2) ◽  
pp. 220-227 ◽  
Author(s):  
C. E. Van Wagner
Keyword(s):  
Computer Simulation ◽  
Exponential Distribution ◽  
Forest Fire ◽  
Fire History ◽  
Class Structure ◽  
Fire Cycle ◽  
Class Distribution ◽  
Age Class ◽  
Negative Exponential Distribution ◽  
Negative Exponential

The expected age-class structure of a forest dependent on random periodic fire for disturbance and renewal is derived and presented. It is simply the negative exponential distribution, well known in probability mathematics. An important feature of this concept is that the present age-class structure of such a forest is the key to its past fire history. Its limitations are discussed, and the computer simulation of variations, including the interaction of fire and logging, is described. Three examples of its use in interpreting fire history are given.

Timber production versus old-growth preservation with endogenous prices and forest age-classes

2004 ◽  
Vol 34 (6) ◽  
pp. 1296-1310 ◽  
Author(s):  
Olli Tahvonen
Keyword(s):  
Environmental Values ◽  
Timber Harvesting ◽  
Timber Production ◽  
Forest Age ◽  
Forest Land ◽  
Age Classes ◽  
Old Growth ◽  
Class Distribution ◽  
Age Class ◽  
Long Run

This study combines timber production and environmental values, applying a dynamic forest-level economic model with any number of forest age-classes. The model includes endogenous timber price or nonlinear harvesting costs and various possibilities to specify the dependence of environmental values (related e.g. to species persistence) on the forest age-class structure. The nonlinearities in the net benefits from timber production have the consequence that fluctuations in optimal timber harvesting may totally vanish or at least become smaller than in forest scheduling models without ad hoc even flow constraints. If environmental values are specified to depend on the fraction of forest land preserved as old growth, the optimal long run allocation between timber production and old growth is represented by an equilibrium continuum. Thus the optimal long run allocation depends on the initial age-class distribution. The continuum and the dependence of initial age-class distribution vanish when the rate of discount approaches zero. If the environmental values of age-classes increase smoothly with age, the long run equilibrium may simultaneously include multiple rotation periods. The model determines the optimality of producing timber and environmental values separately at different parts of the forest or at the same piece of forest land. Numerical computation suggests that the optimal solution always converges toward some optimal long run stationary age-class distribution.

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.

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