AGENDA
Gamma distribution
Exponential distribution
Beta distribution
Weibull distribution
Simulation application
Homework
Quiz

GAMMA DISTRIBUTION

GAMMA DISTRIBUTION

GAMMA DISTRIBUTION

EXPONENTIAL DISTRIBUTION
Gamma distribution with alpha parameter=1
Related to random poisson processes
Poisson distribution was number of observations in a given period of time
Exponential distribution is the time between observations for a poisson process

EXPONENTIAL DISTRIBUTION

EXPONENTIAL DISTRIBUTION

EXPONENTIAL DISTRIBUTION
The exponential distribution function can be integrated and evaluated to obtain cumulative distribution function values

BETA DISTRIBUTION
Continuous random variable that is between 0 and 1
Frequently used in engineering project management
Probability that some task will be completed on time
Parkinson’s law
Student syndrome
Parameters
Alpha
Beta

BETA DISTRIBUTION

BETA DISTRIBUTION

WEIBULL DISTRIBUTION
Found when a random variable is normally distributed, but mean – x standard deviations cannot be less than 0
Parameters
Alpha
Beta

WEIBULL DISTRIBUTION

WEIBULL DISTRIBUTION

SIMULATION
Customers randomly arrive to a service facility with an average of 2 per minute
The average interarrival time is 0.5 minutes
Generate an exponentially distributed random variate that represents this process
Solution - Inverse transformation method
x = -Beta ln (1-F(x))
Generate Unif(0,1)
x = -0.5 ln (1-unif(0,1))

HOMEWORK
5.20, 5.24, 5.26, 5.38, 5.58