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Non-normal probability distributions - Coggle Diagram
Non-normal probability distributions
Normal Probability Curve
Most commonly used in statistics
Described by mean and standard deviation
Symmetrical in nature
Other Discrete Distributions
Negative Binomial Distribution
Geometric Distribution
Weibull Distribution
Describes reliability applications
Can resemble other distributions
Statistical Analysis Tools
Central Limit Theorem allows for analysis of large, randomly-sampled continuous data sets
Use of software like Minitab for analysis
Non-Normal Continuous Distributions
Exponential Distribution
Statistical test: Chi-Squared Goodness-of-Fit
Used for arrival times, time between failures, etc
Data concentrated at one end of the x-axis
Histogram/trend line decreases exponentially
Lognormal Distribution
Always positively skewed
Used for time durations, wealth distribution, etc
Asymmetrical, constrained by zero
Weibull Distribution
Used for reliability applications, failure probabilities
Continuous data related to time
Can resemble other distributions
Other Types of Continuous Distributions
Uniform Distribution: Rare in randomly-sampled data; may indicate measurement issues
Triangular Distribution: Formed using mode and upper/lower limits
Beta Distribution: Flexible, can resemble other distributions
Gamma Distribution: Skewed to the right; encompasses various shapes
Laplace Distribution: Bilateral exponential or double-exponential distribution
Logistic Distribution: Used to approximate other symmetrical distributions
Cauchy Distribution: Elongated normal curve with a tighter peak
Importance in Six Sigma
Tying financial data to events
Identifying areas for improvement
Helps in assessing process performance
Binomial Distribution
Describes attribute data
Assumes independence of trials
Used for discrete data with two outcomes
Other Continuous Distributions
Gamma Distribution
Beta Distribution
Triangular Distribution
Uniform Distribution
Laplace Distribution
Logistic Distribution
Cauchy Distribution
Lognormal Distribution
Describes large range data
Always positively skewed
Asymmetrical
Exponential Distribution
Used for arrival times, time between failures, etc
Decreases exponentially
Poisson Distribution
Describes events occurring at random intervals
Related to the exponential distribution
Used for random occurrences within time or distance
Normal Probability Distributions Revie
Described by mean and standard deviation
Symmetrical curve centered around the mean
Continuous data related to an infinite number of points along an interval
Using Probability Distributions
Understanding event probabilities
Evaluating process improvements
Helps in making data-driven decisions