List of All Probability-and-distributions Formulas

All Probability-and-distributions Formulas List

Statistical Power

Formula:

p = 1 - β


Where,

p = Statistical Power of Test
β = Beta

Related Calculator:

Permutation and Combination

Formula:

Permutation
nPr = n! / ( n - r )!

Combination
nCr = nPr / r!

Related Calculator:


Normal Distribution

Normal Distribution Formula :

X < mean = M - Z
X > mean = M + Z
Z = (X-M) / σ


Where,

M = Mean.
σ = Standard Deviation.
X = Normal Random Variable

Related Calculator:

Probability Density Function of Normal Distribution, Standard Normal Distribution


Formula :
PDF of Normal Distribution = P(x) = (1/(σsqrt(2π)))e-(x-m)2 / (2σ2)
Standard Normal Distribution = P(x) = (1/sqrt(2π))e-(x2 / 2)

Related Calculator:

Binomial Distribution

Formula:

P (X = r) = nCr pr (1-p)n-r


Where,

Combination nCr = ( n! / (n- r)! ) / r!
n = Number of Events
r = Number of Success
p = Probability of Success

Related Calculator:

Negative Binomial Distribution


Negative Binomial Distribution Formula :
Negative Binomial Distribution P(X = r) = n-1Cr-1 pr (1-p)n-r
where,
Combination n-1Cr-1 = ( (n-1)! / ((n-1)-(r-1))! ) / (r-1)!

Related Calculator:

Poisson Distribution

Poisson-distribution Formula:

Poisson Distribution f(x) = eλx / x!

Related Calculator:

Hypergeometric Distribution

Formula:

Hypergeometric Distribution h(x, N, n, k) = [kCx] [N - kCn - x] / [NCn]


Where,

k = Number of Selected Items from the Population Size
x = Random Variable
N = Total Population Size
n = Total Sample Size

Related Calculator:

Z Score to P Value

Formula:

Related Calculator:

Exponential Distribution


Formula:
P(x) = ae-ax,
where,
a is the parameter of the distribution,
x is the random variable,
P(x) is the probability density function.

Related Calculator:

Expected Value E(x)

Formula:

E[x] = n x p


Where,

n is the number of trials,
p is the probability of a successful outcome.

Related Calculator:

Weibull Probability Distribution Function


Formula Used :

Related Calculator:

Beta Distribution Function


Formula Used:
Probability Density Function (pdf) =
Cumulative Distribution Function (cdf) =
where,   
Β(α,β) - Beta Function   
Βx(α,β)- Incomplete Beta Function

Related Calculator:

Cauchy Distribution

Formula Used:

Related Calculator:

Gamma Distribution Function


Formula Used:

Related Calculator:

Laplace Distribution

Formula Used:

Related Calculator:

Continuous Uniform Distribution

Formula Used:
Probability Density =
Lower Cumulative Distribution =
Upper Cumulative Distribution =

Related Calculator:

Weibull Cumulative Distribution, Probability Density

Formula Used:

Related Calculator:

Inverse / Reciprocal Gamma Distribution


Formula Used:
Probability Density Function (pdf) =
Cumulative Distribution Function (cdf) =

Related Calculator:

Diagnostic Post Test Probability


Formula:
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.

Related Calculator:

Multinomial Distribution

Formula:

Related Calculator:

Rayleigh Distribution


Formula:
rayleigh probability formula
rayleigh cumulative formula

Related Calculator:

Gumbel Distribution for PDF, CDF


Formula:
gumbel probability formula
gumbel cumulative formula

Related Calculator:

Geometric Distribution

Formula:

P(x) = qxp


Where ,

p = Probability of success for a single trial
q = Probability of failure for a single trial ( = 1-p )
x = Total Occurrence - 1

Related Calculator:

Dirichlet Multinomial Distribution


Formula:
Dirichlets Multinomial Distribution

Where,

Pr(Z | α ) is Dirichlets Multinominal Distribution
A is ∑k αk (Sigma) represents summation of Parameter vector (α) values
N is ∑k nk represents summation of Independent trial (n) values
k is number of trials
Γ (gamma) represents factorial function of (x-1)
Π (pi) represents product function

Related Calculator:

Standard Distribution


Formula Used:
Mean (M)= Sum of random values / n
Standard Sample Deviation


where,
X - sample values
M - mean value
n - number of samples values

Related Calculator:

Kolmogorov Smirnov Test

Formula:


KS-Test-Formula

Where,

D = Maximum Value of Normal Distribution,
N = Numbeformr of Statistic Data,
F = Kolmogorov Smirnov (KS) Index.

Related Calculator:

Student T Test

Formula:


student t test statistics formula
sample variance

Where

X1 - Group one data,
X2 - Group two data,
t - test statistic
n1,n2 - Group values count

Related Calculator:

Degrees of Freedom

One Sample T-Test Formula:

d = n1 - 1

Two Sample T-Test Formula:

df = (n1 + n2) - 2


Where,

df = Degree of Freedom
n1 = Total Number in Sequence 1
n2 = Total Number in Sequence 2

Related Calculator:

Combination nCr

Formula:

C(n,r) = n! / ( r! (n - r)! )


Where,

C(n,r) = Combinations nCr
n = Number of Sample Points in Set
r = Number of sample Points in Each Combination

Related Calculator:

Fisher Z Transformation

Formula:

Zr = ( 1 / 2 ) [ ln ( 1 + r ) - ln ( 1 - r ) ]
SEzr = ( 1 / √( n - 3 ) )


Where,

Zr = Z Score
SEzr = Standard Error
r = Correlation Coefficient
n = Size

Related Calculator:

Standard Normal Distribution

Formula:

Z = (x - μ) / σ


Where,

Z = Standardized Random Variable
x = The Value that is being Standardized
μ = Mean of the Distribution
σ = Standard Deviation of the Distribution

Related Calculator:

Geometric Probability

Formula:

r = (1 - p)
u = rx
f = u x p
l = 1 - r(x + 1)
m = r / p


Where,

u = Upper CDF
l = Lower CDF
f = Probability of Mass
m = Mean
p = Probability of Success
x = Percentile x

Related Calculator:

Index Of Dispersion

Formula:

Index of Dispersion = σ2 / μ


Where,

μ = Mean
σ2 = Variance

Related Calculator:

Permutation

Formula:

nPr = n! / ( n - r )!


Where,

nPr = Permutations
n = Number of sample points in set n
r = Number of sample points in each permutation

Related Calculator:

T Score

Formula :

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

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


Sample Standard Deviation :
Standard Deviation Formula

Related Calculator:

Log Odds and Odds

Formula:

When Observed Proportion is Given
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

Related Calculator:

Bivariate Distribution

Formula:

Probability Density (f) = ( 1 / ( 2 π √ ( 1 - p2))) × ( e ( - ( x2 - 2pxy + y2)) / ( 2 ( 1 - p2)))


Where,

f = Probability Density
x = Percentile x
y = Percentile y
p = Correlation Coefficient

Related Calculator:

Logistic Distribution

Formula:

E = e- ((x - a) / b)
p = E / (b x (1 + E)2)
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)

Related Calculator:

Number Lock Permutations

Formula:

Combination Without Repitition = a! / b! x (a - b)!
Combination With Repitition = (a + b - 1)! / b! x ((a + b - 1) - b)!
Variation Without Repitition = a! / (a - b)!
Variation With Repitition = ab


Where,

a = Element to Choose from
b = Elements Chosen

Related Calculator:

T Function and V Function

Formula:

t = 1 / (2π) tan-1a


Where,

t = T-Function and V-Function
a = Coefficient (y = ax)

Related Calculator:

Arcsine Distribution

Formula:

Cumulative Distribution Function = (2 / π) * (arcsine (√ (x)))
Probability Distribution Function = 1 / (π √ (x (1 - x)))


Where,

x = Parameter

Related Calculator:

Folded Normal Distribution

Formula:

Folded Normal Distribution

Where,

x = Upper Limit
μ = Mean
σ2 = Variance
erf=Error function

Related Calculator:

Percentile Mean Standard Deviation

Formula:

50th Percentile = Mean
84th Percentile = Mean + Standard Deviation
97.5th Percentile = Mean + (2 x Standard Deviation)

Related Calculator:


english Calculators and Converters


Sitemap