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Non-Normal Probability Distributions - Coggle Diagram
Non-Normal Probability Distributions
Discrete Data
not continuous by nature
categorical occurences
Continuous Data
normal distribution is related
associated with random variables that can take the form of any of an infinite number of points along an interval
Normal Curve
most commonly required for inferential statistics
symmetrical
described statistically using both the mean and standard deviation
curve centers on the mean
number of standard deviations away from the mean changes the probability of the amount of data under the curve
Exponential Distributions
creates a histogram or trend line that is exponential in nature
decreases exponentially as you travel across x-axis
never appears symmetrical
described statistically by the mean of the data and a value known as lambda
Lognormal Distribution
asymmetrical
trend line appears more as a wave that moves across the page
used to describe time durations or distribution of assets
typically describes a data set with values in large ranges
can be described with both mean and standard deviation
always has a positive skew
Wellbull Distribution
relate to continuous data
curves fit lognormal, exponential, and normal distribution
often used when working with reliability applications and failure probabilities
Central Limit Theroem
states that the distribution of the mean of a large, identically distributed number of independent variables will approximate the normal curve
Cauchy Distribution
looks like an elongated normal curve with a tighter peak
Logistical Distribution
appears to approximate the normal curve and used in some science and match functions to approximate other symmetrical distributions
Laplace Distribution
referred to as the bilateral exponential distribution or the double-exponenttial distribution
Uniform Distribution
occurs when data points are divided even among bins
Beta Distribution
can take on a number of shapes, are considered extremely flexible and can become stand-ins for other distributions given certain statistical parameters
Gamma
take on a number of shapes
always skewed right
Binomial Distributions
used when dealing with discrete data and there are only two outcomes for each trial or sample
probability function
p(x)= [(n!)/(x!(n-x!)] p^xq^n-x
Poisson Distribution
used when dealing with data that is distributed randomly within time, distance, or other unit of measurement
Geometric Distribution
used when there are two outcomes for a trial, trials are independent, and there is a waiting time before the first occurrence
Negative Binomial
also used with attribute data: fail/pass and other situations where there are only two outcoomes for each trial