Goodness-of-fit test with modified statistics chi-square

In the paper we continue the research on possibility of using parametric functions that allow unbiased estimates to test a null hypothesis about a kind of distribution by the chi-square test. Based on Wald's method a new asymptotic test is proposed for testing hypothesis according to which the distribution of random value belongs to a one-parameter exponential family. According to a level of complexity this test occupies an intermediate position between the Nikulin-Rao-Robson’s test and the test of moment conditions. Two examples are mentioned as corollaries for the main statement of the paper. Corollary 2.1 contains the result connecting the proposed test statistic with one-dimensional version of the Nikulin-Rao-Robson’s statistic. Corollary 2.2 contains test statistic for testing a null hypothesis about the kind of distribution with a special additional restriction on a hypothetical distribution.