Weibull Distribution Example

Weibull Distribution is a continuous Propability Distribution. It provides accurate failure analysis and risk predictions with extremely small samples using a simple and useful graphical plot. This worksheet help you to understand how to compute weibull distribution. The below formula used to calculate Weibull Distribution,

P(X1 < X < X2) = e-(X1/β)α - e-(X2/β)α

Mean: μ = βΓ(1 + 1/α)

<>bMedian: = β(LN(2))1/α (Natural log of 2)

mode = β(1 - 1/α)1/α

Variance: σ2 = β2[Γ(1 + 2/α) - Γ(1 + 1/α)2]
Note: Value α & β must be Positive.

Example:
Calculate the Weibull Distribution whose α & β is 2 & 5, X1 = 1, X2 = 2.
Substitute these values in the above formulas,
P(X1 < X < X2) = e-(X1/β)α - e-(X2/β)α
P(1 < X < 2) = e-(1/5)2 - e-(2/5)2
= 0.9608 - 0.8521
= 0.1087
Mean:
μ = βΓ(1 + 1/α)
= 5x Γ(1+1/2)
= 5x Γ(1.5)
= 5x 0.8864
= 4.432

Median:
= β(LN(2))1/α
= 5x(0.6932)(1/2)
= 5x0.8326
= 4.1629

Variance:
σ2 = β2[Γ(1 + 2/α) - Γ(1 + 1/α)2]
σ2 = 52[Γ(1 + 2/2) - Γ(1 + 1/2)2]
= 25x[Γ(2)- Γ(1.5)2]
= 25x[1- 0.7857]
= 25X 0.2143
= 5.3575

Standard Deviation:
σ = √variance
= √(5.3575)
= 2.3146

When you try such calculations on your own, this weibull distribution calculator can be used to verify your results of calculations.


Similar Worksheets  Poisson Distribution Example
 Normal Distribution Table
 Exponential Distribution Formula, Example
 Normal Distribution Practice Problems
 Worksheet for how to calculate Negative Binomial Distribution
 Binomial Distribution Worksheet
 Worksheet for how to calculate Hypergeometric Distribution
 Normal Distribution Worksheet

  Probability   Statistics