Pérez, T.Pardo Llorente, Julio Ángel2023-06-202023-06-202003-070932-502610.1007/s00362-003-0160-0https://hdl.handle.net/20.500.14352/50291K-phi-divergence's, statistic family for goodness-of-fit, under the null hypothesis, has an asymptotic chi-squared distribution; however, for small samples, the chi-squared approximation in some cases does not well agree with the exact distribution. In this paper, a closer approximation to the exact distribution is obtained by extracting the phi-dependent second order component from the distribution. Moreover, numerical results are presented for moderate sample sizes with moderate number of cells.engjournal articlehttp://link.springer.com/content/pdf/10.1007%2Fs00362-003-0160-0content/pdf/10.1007%2Fs00362-003-0160-0http://link.springer.com/restricted access519.22K-phi-divergencegoodness-of-fitsecond order limit distribution.Estadística matemática (Matemáticas)1209 Estadística