Unit Mean and Constant Variance of the Generalized Gamma Distribution after Square Root Transformation in Statistical modeling

In this paper, we studied the effect of square root transformation on the error component of the multiplicative error model whose distribution belongs to the generalized gamma family. The purpose of the study is to determine the effect of the said transformation on the basic assumptions; unit mean and constant variance required for statistical modeling. The special cases of the Generalized Gamma Distribution considered are the three-parameter Gamma distribution error component, the Chi-square, Exponential, Weibull, Rayleigh and Maxwell distributed error components. From the results of the study, the unit mean assumption is approximately maintained for all the distributions. It was also found that there were reduction in the variances of all the square root transformed distributions under study except those of the Gamma(a, b, 1), when a > 1, Rayleigh and Maxwell distributions that increased. Therefore we conclude that square root transformation is not appropriate for multiplicative error models with either a Gamma (a, b, 1), for a > 1 or Rayleigh or Maxwell distributed error component. Finally square root transformations where applicable are successful for the distributions under study if the variance of the transformed data < 0.5. Keywords: Generalized gamma distribution; Square root transformation; Mean; Variance; multiplicative error Model; Error componen

The new class of Kummer beta generalized distributions

Ng and Kotz (1995) introduced a distribution that provides greater flexibility to extremes.We define and study a new class of distributions called the Kummer beta generalized family to extend the normal, Weibull, gamma and Gumbel distributions, among several other well-known distributions. Some special models are discussed. The ordinary moments of any distribution in the new family can be expressed as linear functions of probability weighted moments of the baseline distribution. We examine the asymptotic distributions of the extreme values. We derive the density function of the order statistics, mean absolute deviations and entropies. We use maximum likelihood estimation to fit the distributions in the new class and illustrate its potentiality with an application to a real data set

Ajuste de distribuição de probabilidades de variáveis de custo fixo e variável na produção de suínos no estado de Santa Catarina

Agribusiness is an extremely important sector in the world economy and in the brazilian economy, as it generates employment and income. Among the agribusiness sector products stand out sugar, coffee, soybean, corn, beef, swine, chicken and others. The research hereby presented is based on a real database from pig farming. Swine producers are constantly seeking for higher profits, in other words, they always try to obtain an expected maximum return on investment. Therefore it is necessary determine the behavior of the costs (fixed and variable) involved in the production. Since the random variable cost is a continuous variable, this research aimed to test the probability distributions for continuous variables, as Weibull, Rayleigh, Lognormal and Normal - identifying which of them have the best fit through the QQ-plot graph and p-values of the Kolmogorov-Smirnov test with probability 0,05. The Weibull distribution showed a better adjustment to variable total cost due to present p-value of 0,1867 in Kolmogorv-Smirnov test. For fixed cost total, the Rayleigh distribution adjusted the data better showing a p-value of 0,2910. It is suggested as a complement to this study, perform the same analysis with continuous probability distributions using deflated data, this way should be find the best distribution for the data.Trabalho de Conclusão de Curso (Graduação)O agronegócio é um setor de extrema importância tanto na economia mundial quanto na brasileira, pois participa da geração de emprego e renda. Dentre os produtos no setor de agronegócios, destacam-se produção de açúcar, café, soja, milho, carnes bovina, suína e frango, entre outros. O presente estudo irá focar em dados provindos da suinocultura. Os produtores de carne suína estão cada dia mais em busca de rentabilidade, ou seja, obter um retorno máximo esperado sobre o investimento realizado, com isso faz-se necessário conhecer o comportamento dos custos (variáveis e fixos) envolvidos na produção. Sendo a variável custo uma variável contínua, o presente trabalho teve por objetivo testar as distribuições de probabilidades para variável contínua, como Weibull, Rayleigh, Log-normal e Normal e, identificar qual delas terá o melhor ajuste através do gráfico QQ-plot e p-valores do teste de Kolmogorov-Smirnov à nível de 0,05 de probabilidade. A distribuição Weibull apresentou melhor ajuste para a variável custo variável total devido apresentar p-valor igual a 0,1867 no teste de Kolmogorov-Smirnov. Para a variável custo fixo total a distribuição Rayleigh ajustou-se melhor aos dados apresentanto um p-valor de 0,2910. Sugere-se como complemento para este estudo, executar as mesmas análises com as distribuições contínuas de probabilidade usando os dados deflacionados, dessa forma encontra-se-á a distribuição que se ajustará a todos os dados