Yule-Simon distribution

Yule-Simon distribution (tsz. Yule-Simon distributions)

1. (matematika) ?

The Yule-Simon distribution models phenomena with power-law behavior, such as word frequencies or city sizes. Its probability mass function is:

$${\displaystyle P(k)=\alpha \,{\text{Beta}}(k,\alpha +1)}$$

with ${\textstyle \alpha >0}$ as the shape parameter. It has a heavy tail, meaning a few events are very common while many are rare. It’s used in areas like linguistics (Zipf’s law), ecology, and economics.

Key stats:

• Mean: ${\textstyle {\frac {\alpha }{\alpha -1}}}$ (if ${\textstyle \alpha >1}$)
• Variance: ${\textstyle {\frac {\alpha ^{2}}{(\alpha -1)^{2}(\alpha -2)}}}$ (if ${\textstyle \alpha >2}$)

• Yule-Simon distribution - Szótár.net (en-hu)
• Yule-Simon distribution - Sztaki (en-hu)
• Yule-Simon distribution - Merriam–Webster
• Yule-Simon distribution - Cambridge
• Yule-Simon distribution - WordNet
• Yule-Simon distribution - Яндекс (en-ru)
• Yule-Simon distribution - Google (en-hu)
• Yule-Simon distribution - Wikidata
• Yule-Simon distribution - Wikipédia (angol)