Definição da função densidade de probabilidade com distribuição Weibull intervalar e aplicação de diferentes métodos de integração

Abstract

When calculations are performed in a computational system, floating-point numbers are used, that makes with it isn’t possible to represent the values correctly. One of the alternatives to avoid errors caused by the machine is the use of interval arithmetic, which guarantees a interval solution where the real value is contained. To obtain the numerical value of probability density functions of continuous random variable with Weibull distribution, is required the solution of integrals, in which the solution is obtained through aproximation, which makes it subject to errors, such as rounding and truncation errors. This work intends to define the probability density funcion with Weibull distribution in interval form, using the interval extension method. After the definition is obtained, the function with Weibull distribution was implemented using different methods to solve interval integrals already existing in literature, in order to analise which method returns a better quality solution interval. To verify the obtained results, a error analysis was done through the absolute and relative error. Furthermore, the implemented algorithm complexity will also be analyzed, in order to verify the computational effort when using interval arithmetic is similar to the effort spent with the calculations using real entrances. With the results, it was possible to determinate that the method to solve interval integrals with the best results was the interval primitive of the function, while the interval integration method that showed better results was the Interval Simpson method.