1. Chapter 14 Fitting Probability Distributions
BAE 5333 Applied Water Resources Statistics
Biosystems and Agricultural Engineering Department
Division of Agricultural Sciences and Natural Resources
Oklahoma State University

2. Probability Distributions - Minitab
Chi-Square
Normal F T
Uniform
Binomial
Geometric
Negative Binomial
Hypergeometric
Discrete
Integer
Poisson
Beta
Chauchy
Exponential
Gamma
Laplace
Largest Extreme Value
Logistics
Loglogistics
Lognormal
Smallest Extreme Value
Triangular
Weibull

3. Probability Distributions Basic Types of Parameters
Location
Specifies the x-axis location
Changing results in a shift to left or right
Scale
Specifies the form
Changing compresses or expands the distribution without altering its basic shape
Shape
Specifies the basic shape
Number of shape parameters: 0, 1 or 2

4. Probability Density Function (pdf) Normal (Gaussian) Distribution
X = continuous variable
μ = mean (Location Parameter)
σ2 = variance (Scale Parameter)

5. Lognormal Distribution
X = continuous variable
μ = mean (Location Parameter)
σ2 = variance (Scale Parameter)

6. Exponential Distribution
X = continuous variable
λ = Scale Parameter

7. Weibull Distribution Two Parameter X = continuous variable
θ = Location Parameter
λ = Scale Parameter
k = Shape Parameter
Two Parameter

8. Uniform and Triangular Distributions

9. Pearson’s Chi Square Goodness-of-Fit Test
Χ = Test Statistic
Oi = Observed data
Ei = Theoretical (expected) data
n = Number of data points
Null Hypothesis
H0: Data follow the distribution
H1: Data do not follow the distribution
Compares a theoretical frequency distribution with data.
Observed data are assumed independent
Results may not be accurate if the expected frequency of any bin is less than 5.

10. MINITAB
Laboratory 15