Aplicação do método da imagem intervalar nas funções densidade de probabilidade das variáveis aleatórias contínuas

Abstract

When we work with numerical calculations in computational environments, we operate on floating-point numbers. Thus, the result is only an approximation of a real value and erros generated by rounding or truncations can lead to incorrect results, and the accuracy of the estimated responses can not be affirmed without the aid of an error analysis. By using intervals to represent real values, it becomes possible to control the propagation of these errors, because interval results carry with them the safety of their quality. To transform the interval function from a real function, the interval extension method is usually used. Statistical work shows that the complexity of the algorithms using the interval image method is much greater than using the interval extension method, but there is still no analysis regarding the use of the interval image method applied in the functions with probability distribution. In this context, the present work aims to use the interval image method, instead of the interval extension, to solve the probability density functions with interval inputs, in order to obtain more accurate results in a reasonable processing time. As a last objective, computational complexities were analysed to compute such functions with the interval image method. As a result, it is ensured that when using the interval image method, in some examples the solution intervals were returned with smaller diameter, but the computational effort increased from a constant order to a exponential order.