Where,

p = Statistical Power of Test

β = Beta

X > mean = M + Z

Z = (X-M) / Ï

Where,

M = Mean.

Ï = Standard Deviation.

X = Normal Random Variable

PDF of Normal Distribution = P(x) = (1/(σsqrt(2π)))e

Standard Normal Distribution = P(x) = (1/sqrt(2π))e

Where,

Combination

n = Number of Events

r = Number of Success

p = Probability of Success

Negative Binomial Distribution P(X = r) =

where,

Combination

Where,

k = Number of Selected Items from the Population Size

x = Random Variable

N = Total Population Size

n = Total Sample Size

P(x) = ae

where,

a is the parameter of the distribution,

x is the random variable,

P(x) is the probability density function.

Where,

n is the number of trials,

p is the probability of a successful outcome.

Probability Density Function (pdf) =

Cumulative Distribution Function (cdf) =

where,

Β(α,β) - Beta Function

Β

Probability Density =

Lower Cumulative Distribution =

Upper Cumulative Distribution =

Probability Density Function (pdf) =

Cumulative Distribution Function (cdf) =

O = p1 / ( 1 - p1 ),

p2 = O * L,

p = p2 / ( 1 + p2 ),

Where,

p1 is the pretest probability,

O is the pretest odds,

p2 is the posttest odds,

L is the likelihood ratio,

p is the posttest probability.

Where ,

p = Probability of success for a single trial

q = Probability of failure for a single trial ( = 1-p )

x = Total Occurrence - 1

Where,

Pr(Z | α ) is Dirichlets Multinominal Distribution

A is ∑

N is ∑

k is number of trials

Γ (gamma) represents factorial function of (x-1)

Π (pi) represents product function

Mean (M)= Sum of random values / n

X - sample values

M - mean value

n - number of samples values

Where,

D = Maximum Value of Normal Distribution,

N = Numbeformr of Statistic Data,

F = Kolmogorov Smirnov (KS) Index.

Where

X

X

t - test statistic

n1,n2 - Group values count

Where,

df = Degree of Freedom

n

n

Where,

C(n,r) = Combinations nCr

n = Number of Sample Points in Set

r = Number of sample Points in Each Combination

SE

Where,

Z

SE

r = Correlation Coefficient

n = Size

Where,

Z = Standardized Random Variable

x = The Value that is being Standardized

μ = Mean of the Distribution

σ = Standard Deviation of the Distribution

u = r

f = u x p

l = 1 - r

m = r / p

Where,

u = Upper CDF

l = Lower CDF

f = Probability of Mass

m = Mean

p = Probability of Success

x = Percentile x

Where,

μ = Mean

σ

Where,

n = Number of sample points in set n

r = Number of sample points in each permutation

t - Observed = (Sample Mean - Population Mean) / Standard Deviation

Mean = Sum of X values / N(Number of Values)

o = p / (1 - p)

l = log (p / (1 - p))

When Odds is Given

p = o / (1 + o)

l = log(o)

When Log Odds is Given

o = Exp (l)

p = o / (1 - o)

Where,

o = Odds

l = Log Odds

p = Observed Proportion

Where,

f = Probability Density

x = Percentile x

y = Percentile y

p = Correlation Coefficient

p = E / (b x (1 + E)

lcdf = 1 / (1 + E)

ucdf = 1- lcdf

Where,

E = Exponent Value

x = Percentile

a = Location Parameter

b = Scale Parameter

p = Probability Density Function (pdf)

lcdf = Lower Cumulative Density Function (lcdf)

ucdf = Upper Cumulative Density Function (ucdf)

Combination With Repitition = (a + b - 1)! / b! x ((a + b - 1) - b)!

Variation Without Repitition = a! / (a - b)!

Variation With Repitition = a

Where,

a = Element to Choose from

b = Elements Chosen

Where,

t = T-Function and V-Function

a = Coefficient (y = ax)

Probability Distribution Function = 1 / (π √ (x (1 - x)))

Where,

x = Parameter

Where,

x = Upper Limit

μ = Mean

σ

erf=Error function

84th Percentile = Mean + Standard Deviation

97.5th Percentile = Mean + (2 x Standard Deviation)