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https://github.com/danmadeira/algoritmos-estatistica-pl-sql

Demonstração de Algoritmos de Estatística em PL/SQL
https://github.com/danmadeira/algoritmos-estatistica-pl-sql

algorithms data-analysis data-science database oracle oracle-database pl-sql statistics

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Demonstração de Algoritmos de Estatística em PL/SQL

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README 

          
## Demonstração de Algoritmos de Estatística em PL/SQL



Esta é uma demonstração de funções que implementam alguns cálculos estatísticos. Os algoritmos que representam as fórmulas estatísticas estão escritos em uma estrutura simples e semelhante a aplicação pura das respectivas fórmulas, para deixar o código o mais limpo possível, e assim, didático.



Até o momento, estas são algumas das fórmulas estatísticas que estão presentes:



* Média Aritmética

## $$\mu = \frac{1}{n} \sum_{i=1}^{n} x_i$$



* Média Aritmética Ponderada

## $$\mu_p = \frac{1}{\sum_{i=1}^{n} w_i} \sum_{i=1}^{n} w_i x_i$$



* Média Geométrica

## $$\mu_g = \sqrt[n]{\prod_{i=1}^{n} x_i}$$



* Média Geométrica Ponderada

## $$\mu_{gp} = \sqrt[\sum_{i=1}^{n} w_i]{\prod_{i=1}^{n} {x_i}^{w_i}}$$



* Média Harmônica

## $$\mu_h = \frac{n}{\sum_{i=1}^{n} \frac{1}{x_i}}$$



* Média Harmônica Ponderada

## $$\mu_{hp} = \frac{\sum_{i=1}^{n} w_i}{\sum_{i=1}^{n} \frac{w_i}{x_i}}$$



* Média Quadrática

## $$\mu_q = \sqrt{\frac{1}{n} \sum_{i=1}^{n} {x_i}^2}$$



* Média Quadrática Ponderada

## $$\mu_{qp} = \sqrt{\frac{1}{\sum_{i=1}^{n} w_i} \sum_{i=1}^{n} w_i{x_i}^2}$$



* Média Cúbica

## $$\mu_c = \sqrt[3]{\frac{1}{n} \sum_{i=1}^{n} {x_i}^3}$$



* Média Cúbica Ponderada

## $$\mu_{cp} = \sqrt[3]{\frac{1}{\sum_{i=1}^{n} w_i} \sum_{i=1}^{n} w_i {x_i}^3}$$



* Média Desarmônica

## $$\mu_d = \frac{2}{\frac{1}{\frac{\sum_{i=1}^{n} x_i}{n}} + \frac{1}{\frac{{\bigl(\frac{\sum_{i=1}^{n} x_i}{n}\bigl)}^2}{\frac{n}{\sum_{i=1}^{n} \frac{1}{x_i}}}}}$$



* Média Desarmônica Ponderada

## $$\mu_{dp} = \frac{2}{\frac{1}{\frac{\sum_{i=1}^{n} w_i x_i}{\sum_{i=1}^{n} w_i}} + \frac{1}{\frac{{\Bigl(\frac{\sum_{i=1}^{n} w_i x_i}{\sum_{i=1}^{n} w_i}\Bigl)}^2}{\frac{\sum_{i=1}^{n} w_i}{\sum_{i=1}^{n} \frac{w_i}{x_i}}}}}$$



* Mediana



* Moda



* Desvio Absoluto Médio

## $$D_{am} = \frac{1}{n} \sum_{i=1}^{n} |x_i - \mu|$$



* Desvio Absoluto Mediano

## $$D_{am} = Md(|x_i - \tilde{x}|)$$



* Variância Populacional

## $$\sigma^2 = \frac{1}{n} \sum_{i=1}^{n} (x_i - \mu)^2$$



* Desvio Padrão Populacional

## $$\sigma = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (x_i - \mu)^2}$$



* Variância Amostral

## $$s^2 = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2$$



* Desvio Padrão Amostral

## $$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2}$$



* Variância Populacional (para dados agrupados)

## $$\sigma^2 = \frac{1}{\sum_{i=1}^{n} w_i} \sum_{i=1}^{n} \bigl((x_i - \mu)^2 w_i\bigl)$$



* Desvio Padrão Populacional (para dados agrupados)

## $$\sigma = \sqrt{\frac{1}{\sum_{i=1}^{n} w_i} \sum_{i=1}^{n} \bigl((x_i - \mu)^2 w_i\bigl)}$$



* Variância Amostral (para dados agrupados)

## $$s^2 = \frac{1}{\sum_{i=1}^{n} w_i - 1} \sum_{i=1}^{n} \bigl((x_i - \bar{x})^2 w_i\bigl)$$



* Desvio Padrão Amostral (para dados agrupados)

## $$s = \sqrt{\frac{1}{\sum_{i=1}^{n} w_i - 1} \sum_{i=1}^{n} \bigl((x_i - \bar{x})^2 w_i\bigl)}$$



* Coeficiente de Variação

## $$CV = \frac{\sigma}{\mu} \times 100$$



* Coeficiente de Variação (para dados agrupados)

## $$CV = \frac{\sigma}{\mu} \times 100$$



* Covariância Populacional

## $$\sigma_{xy} = \frac{1}{n} \sum_{i=1}^{n} (x_i - \mu_x)(y_i - \mu_y)$$



* Covariância Amostral

## $$s_{xy} = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})$$



* Coeficiente de Correlação Populacional de Pearson

## $$\rho_{xy} = \frac{\sigma_{xy}}{\sigma_x \sigma_y}$$



* Coeficiente de Correlação Amostral de Pearson

## $$r_{xy} = \frac{s_{xy}}{s_x s_y}$$



* Somatório dos Quadrados

## $$SS_x = \sum_{i=1}^{n} {x_i}^2 - \frac{(\sum_{i=1}^{n} x_i)^2}{n}$$



* Somatório dos Produtos XY

## $$SS_{xy} = \sum_{i=1}^{n} x_i y_i - \frac{(\sum_{i=1}^{n} x_i)(\sum_{i=1}^{n} y_i)}{n}$$



* Coeficiente de Correlação de Pearson

## $$r = \frac{SS_{xy}}{\sqrt{SS_x \times SS_y}}$$



* Z-score Populacional

## $$z = \frac{x - \mu}{\sigma}$$



* Z-score Amostral

## $$z = \frac{x - \bar{x}}{s}$$



* Três Desvios



* Amplitude



* Assimetria

## $$A = \frac{1}{n} \sum_{i=1}^{n} \Bigl(\frac{x_i - \bar{x}}{s}\Bigl)^3$$



* Curtose

## $$K = \frac{1}{n} \sum_{i=1}^{n} \Bigl(\frac{x_i - \bar{x}}{s}\Bigl)^4 - 3$$



* Quartis

## $$i = \frac{j(n+1)}{4}$$

## $$Q_j = x_i + \biggl(\frac{j(n+1)}{4} - i\biggl) (x_{i+1} - x_i)$$

*para j = 1, 2 e 3*



Além de funções para:



* Desagrupar dados

* Agrupar dados

* Ordenar dados

* Ordenar frequências



Obs.: As funções possuem versões para dados agrupados ou não agrupados e para dados amostrais ou populacionais. Há também um script de exemplo, com demonstrações das chamadas das funções.



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