example of syntax in python

https://www.youtube.com/watch?v=JWtOYWSVYOE

PrivateView

PYTHON (7 Weekends Batch) tutorials - YouTube

PYTHON (CORE & ADVANCED) (7 Weekends Batch) tutorials || by Mr. Prakash Babu On 24-05-2025 @8AM ISTCourse Content: https://bit.ly/3hbLZR5=====...

https://en.wikipedia.org/wiki/Dirichlet_distribution

PrivateView

Dirichlet distribution - Wikipedia

Illustrating how the log of the density function changes when K = 3 as we change the vector α from α = (0.3, 0.3, 0.3) to (2.0, 2.0, 2.0), keeping all the individual 's equal to each other.. The Dirichlet distribution of order K ≥ 2 with parameters α 1, ..., α K > 0 has a probability density function with respect to Lebesgue measure on the Euclidean space R K−1 given by

Searches related to example of syntax in python

basic syntax of python programming

python syntax with sample program

python examples for beginners

python syntax explained

script examples in python

list of syntax in python

Searches related to example of syntax in python

basic syntax of python programming

python syntax with sample program

python examples for beginners

python syntax explained

script examples in python

list of syntax in python

Dirichlet distribution

Wikipedia

Fact sheet

Beta

Dirichlet distribution

Parameters

K ≥ 2 {\displaystyle K\geq 2} number of categories (integer) α = (α 1, …, α K) {\displaystyle {\boldsymbol {\alpha }}=(\alpha _{1},\ldots,\alpha _{K})} concentration parameters, where α i > 0 {\displaystyle \alpha _{i}>0}

Support

x 1, …, x K {\displaystyle x_{1},\ldots,x_{K}} where x i ∈ {\displaystyle x_{i}\in } and ∑ i = 1 K x i = 1 {\displaystyle \sum _{i=1}^{K}x_{i}=1}

PDF

1 B (α) ∏ i = 1 K x i α i − 1 {\displaystyle {\frac {1}{\mathrm {B} ({\boldsymbol {\alpha }})}}\prod _{i=1}^{K}x_{i}^{\alpha _{i}-1}} where B (α) = ∏ i = 1 K Γ (α i) Γ (α 0) {\displaystyle \mathrm {B} ({\boldsymbol {\alpha }})={\frac {\prod _{i=1}^{K}\Gamma (\alpha _{i})}{\Gamma {\bigl (}\alpha _{0}{\bigr)}}}} where α 0 = ∑ i = 1 K α i {\displaystyle \alpha _{0}=\sum _{i=1}^{K}\alpha _{i}}

Mean

E = α i α 0 {\displaystyle \operatorname {E} ={\frac {\alpha _{i}}{\alpha _{0}}}} E = ψ (α i) − ψ (α 0) {\displaystyle \operatorname {E} =\psi (\alpha _{i})-\psi (\alpha _{0})} (where ψ {\displaystyle \psi } is the digamma function)

Mode

x i = α i − 1 α 0 − K, α i > 1. {\displaystyle x_{i}={\frac {\alpha _{i}-1}{\alpha _{0}-K}},\quad \alpha _{i}>1.}

Variance

Var = α ~ i (1 − α ~ i) α 0 + 1, {\displaystyle \operatorname {Var} ={\frac {{\tilde {\alpha }}_{i}(1-{\tilde {\alpha }}_{i})}{\alpha _{0}+1}},} Cov = δ i j α ~ i − α ~ i α ~ j α 0 + 1 {\displaystyle \operatorname {Cov} ={\frac {\delta _{ij}\,{\tilde {\alpha }}_{i}-{\tilde {\alpha }}_{i}{\tilde {\alpha }}_{j}}{\alpha _{0}+1}}} where α ~ i = α i α 0 {\displaystyle {\tilde {\alpha }}_{i}={\frac {\alpha _{i}}{\alpha _{0}}}}, and δ i j {\displaystyle \delta _{ij}} is the Kronecker delta

Entropy

H (X) = log B (α) {\displaystyle H(X)=\log \mathrm {B} ({\boldsymbol {\alpha }})} + (α 0 − K) ψ (α 0) − {\displaystyle +(\alpha _{0}-K)\psi (\alpha _{0})-} ∑ j = 1 K (α j − 1) ψ (α j) {\displaystyle \sum _{j=1}^{K}(\alpha _{j}-1)\psi (\alpha _{j})} with α 0 {\displaystyle \alpha _{0}} defined as for variance, above; and ψ {\displaystyle \psi } is the digamma function

Method of moments

α i = E (E (1 − E) V − 1) {\displaystyle \alpha _{i}=E\left({\frac {E(1-E)}{V}}-1\right)} where j {\displaystyle j} is any index, possibly i {\displaystyle i} itself

New! PrivateView

Youtube

Your search and this result

New! PrivateView

Wikipedia

Your search and this result

Fact sheet

Parameters

Support

PDF

Mean

Mode

Variance

Entropy

Method of moments

PrivateView

PrivateView

Not available yet!