Exponential distribution - poisson distribution function, Civil Engineering

Exponential distribution - Poisson distribution function:

Let X follow exponential distribution with parameter θ. Find the pdf of

Y = X1/β where  β( ≥ 1 ) is a constant.

Solution :

The function Y = X1/β is one to one in the interval ( 0,∞) where pdf of X is non zero. The inverse of the transformation Y = X1/β is X - Yβ which gives dX/dY =β Yβ-1. Also

fx(x) = 1/θ e-x/θ , x> 0.

Hence

f(y) = f(g-1(y))¦ dg-1(y)/dy ¦

=1/θ e -yβ/θ ¦β yβ-1¦, y>0

and the pdf is

f(y) = β y β -1/θ e -yP/θ , y>0 with parameters θ >0,β ≥ 1

Remark:

The distribution of Y, just derived Example 4, is known as Weibull distribution. That has application is life testing. Remember that if Y follows Weibull distribution with parameters θ and β then Yβ follows the exponential distribution with parameter θ.

The treatment of distribution of functions of more than one variable is similar. However, care should be taken to determine the correct region of variation of the variables under the transformation and use it properly for obtaining the marginal distributions. We assume an example to illustrate the point.

Posted Date: 1/30/2013 7:08:55 AM | Location : United States







Related Discussions:- Exponential distribution - poisson distribution function, Assignment Help, Ask Question on Exponential distribution - poisson distribution function, Get Answer, Expert's Help, Exponential distribution - poisson distribution function Discussions

Write discussion on Exponential distribution - poisson distribution function
Your posts are moderated
Related Questions
plane table surveying is used commonly to survey small areas because

SHEAR STRESS DISTRIBUTION INTO CIRCULAR SECTION DERIVATION

principle of direct levelling

I am a Civil Engg student. Why CBR Values determined only at 2.5 and 5 mm penetration ?.

how to use mood diagram to get f and other Re

Define the Coefficient of Permeability: (K) A measurement of the ability of the soil or an aquifer for the movement of water through it. Also termed "hydraulic conductivity", C

random rubble coursed, suare rubble coursed and uncoursed, polygonal walling, flint walling

Elaborate the term - Prestressed concrete pipes Liquid retaining structures, such as circular pipes, tanks and pressure vessels are suited for circular prestressing. The circum

Define the Types of Transmission in Ultrasonic System? Types of Transmission Three Types of Transmission through the testing element is possible, namely: - Direct transmi

Bricks may be broadly classified as following: Paving bricks Building bricks Special bricks A.   Fire bricks B.   Building Bricks: These bricks are utilized fo