scholarly journals An Inductive Approach to Calculate the MLE for the Double Exponential Distribution

2009 ◽  
Vol 8 (2) ◽  
pp. 594-596
Author(s):  
W. J. Hurley
Keyword(s):  
Exponential Distribution ◽  
Double Exponential Distribution ◽  
Inductive Approach ◽  
Double Exponential

Extremes for the minimal spanning tree on normally distributed points

1998 ◽  
Vol 30 (03) ◽  
pp. 628-639 ◽  
Author(s):  
Mathew D. Penrose
Keyword(s):  
Normal Distribution ◽  
Exponential Distribution ◽  
Spanning Tree ◽  
Dimensional Space ◽  
Edge Length ◽  
Nearest Neighbour ◽  
Minimal Spanning Tree ◽  
Double Exponential Distribution ◽  
Double Exponential ◽  
Union Of Balls

Let n points be placed independently in ν-dimensional space according to the standard ν-dimensional normal distribution. Let M n be the longest edge-length of the minimal spanning tree on these points; equivalently let M n be the infimum of those r such that the union of balls of radius r/2 centred at the points is connected. We show that the distribution of (2 log n)1/2 M n - b n converges weakly to the Gumbel (double exponential) distribution, where b n are explicit constants with b n ~ (ν - 1)log log n. We also show the same result holds if M n is the longest edge-length for the nearest neighbour graph on the points.

Stochastic Description of Loads on the Steel Storage Capacities

2019 ◽  
Vol 968 ◽  
pp. 528-533
Author(s):  
Olexandr Lapenko ◽  
Anton Makhinko ◽  
Nataliia Makhinko
Keyword(s):  
Random Process ◽  
Exponential Distribution ◽  
General Procedure ◽  
Statistical Characteristics ◽  
Random Load ◽  
Double Exponential Distribution ◽  
Double Exponential ◽  
Analytical Formulas ◽  
Normal Law ◽  
Characteristic Maximum

This paper deals with the study of stochastic parameters of external loads, which are used in the tasks of determining the level of reliability of steel storage capacities. To describe the random load process, the normal law and the double exponential distribution of Gumbel were used. It was formulated the technique of transition from the study of the entire random process to the consideration of its maximums. It was obtained quantitative values of the stochastic characteristics of snow and wind loads on the territory of Ukraine, without reference to the zoning maps. A general procedure for determining the probability of failure was formulated, depending from a given characteristic maximum. This index corresponds to the basic level of load. The average intersection of this level by a random load process is equal to one. Analytical formulas are obtained to determine the scale and position of the double exponential distribution of Gumbel, which depend on the characteristic maximum, as well as formulas, which help to calculate the statistical characteristics (standard, expected value and coefficient of variation) of the random value of the load maximums. The possibility of using this approach is theoretically confirmed when the density distribution of the ordinate of a random process follows the normal law. It was proposed expressions for the parameters of the distribution maximums of the random processes, which are described by the polynomial exponent and the Weibull law.

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