Laplace function and other tabular statistical functions: count in Excel

When solving such typical problems of mathematical statistics as building confidence intervals or testing hypotheses about the parameters of random variables, several tabular functions are widely used, for example, the Laplace function or the quantile of the chi-square distribution.

Nowadays, it is not necessary to apply for the missing values ​​in the formula to thick reference books with statistical tables, everything can be calculated directly in Excel:

Formula =НОРМСТРАСП(x)-0,5 calculates the value of the Laplace function of the argument x (substitute the corresponding cell for x ). In this case, Ф(-x)=-Ф(x) , and for x>3,85 value of Ф(x)=0,5 .

Calculate the value of the inverse Laplace function of the argument x can be the formula =НОРМСТОБР(x) . In Excel, the NORMSOBR function (1-eps / 2) will give the required critical value corresponding to a criterion significance level equal to eps. For example, for a criterion with a critical level of 0.05 (5%), the formula NORMSOBR (1-0.05 / 2) = 1.96

Critical points of the t-test can be calculated using the formula =СТЬЮДРАСПОБР(α,n) , where α is the significance level (probability γ or reliability 1-γ ), n is the number of degrees of freedom (for example, the sample size in problems on building confidence intervals) . When the number of degrees of freedom n≥30 distribution reduces to normal with parameters α=0 , σ=корень(n/(n-2)) .

The critical points of the Pearson χ 2 distribution can be calculated using the formula =ХИ2ОБР(a,n) , where a is the significance level, n is the number of degrees of freedom.

The value of the Poisson distribution density function can be =ПУАССОН(n,λ,0) using the formula =ПУАССОН(n,λ,0) , where n is the number of degrees of freedom (number of events), λ is the average number of occurrences of the event (expected numerical value).

In some cases, for calculating with the given value of the parameter γ function Excel, you may need to pass the argument of the function α=1-γ , see carefully the built-in function help.

Student's t distribution

TINV (1-0.95; 9)