MATRIX cumulative distribution functions

The following functions give the probability that a random variable with the specified distribution will be less than quant, the first argument. All functions accept matrix, vector, or scalar as the first argument. All functions except CDF.BVNOR accept only scalar as the second argument. The result has the same dimension as the first argument. Note the period in each function name.

CDF.BERNOULLI. CDF.BERNOULLI(quant, prob). Numeric. Returns the cumulative probability that a value from the Bernoulli distribution, with the given probability parameter, will be less than or equal to quant.

CDF.BETA. CDF.BETA(quant, shape1, shape2). Numeric. Returns the cumulative probability that a value from the Beta distribution, with the given shape parameters, will be less than quant.

CDF.BINOM. CDF.BINOM(quant, n, prob). Numeric. Returns the cumulative probability that the number of successes in n trials, with probability prob of success in each, will be less than or equal to quant. When n is 1, this is the same as CDF.BERNOULLI.

CDF.BVNOR. CDF.BVNOR(quant1, quant2, corr). Numeric. Returns the cumulative probability that a value from the standard bivariate normal distribution, with the given correlation parameter, will be less than quant1 and quant2.

Both the first and second arguments can be matrices or vectors, in which case they should have the same dimensions and the result will have the same dimension as either of these arguments. It is possible that either first or second argument is a matrix or vector, and the other argument is scalar. In this case, the result has the same dimension as the matrix/vector. It is also possible that both the first and second arguments are scalars (in which case, the result will be scalar). The function's third argument should always be scalar.

CDF.CAUCHY. CDF.CAUCHY(quant, loc, scale). Numeric. Returns the cumulative probability that a value from the Cauchy distribution, with the given location and scale parameters, will be less than quant.

CDF.CHISQ. CDF.CHISQ(quant, df). Numeric and same as CHICDF. Chi-square cumulative distribution function of elements. Takes two arguments, a matrix of chi-square values and a scalar giving the degrees of freedom (which must be positive). Returns a matrix having the same dimensions as the first argument, containing the values of the cumulative chi-square distribution function for each of its elements. If an element of the first argument is x and the second argument is S, the corresponding element of the result is a number between 0 and 1, giving the proportion of a chi-square distribution with S degrees of freedom that is less than x. If x is not positive, the result is 0.

CDF.EXP. CDF.EXP(quant, scale). Numeric. Returns the cumulative probability that a value from the exponential distribution, with the given scale parameter, will be less than quant.

CDF.F. CDF.F(M,S1,S2). Numeric and same as FCDF. Cumulative F distribution function of elements. Takes three arguments, a matrix of F values and two scalars giving the degrees of freedom (which must be positive). Returns a matrix having the same dimensions as the first argument M, containing the values of the cumulative F distribution function for each of its elements. If an element of the first argument is x and the second and third arguments are S1 and S2, the corresponding element of the result is a number between 0 and 1, giving the proportion of an F distribution with S1 and S2 degrees of freedom that is less than x. If x is not positive, the result is 0.

CDF.GAMMA. CDF.GAMMA(quant, shape, scale). Numeric. Returns the cumulative probability that a value from the Gamma distribution, with the given shape and scale parameters, will be less than quant.

CDF.GEOM. CDF.GEOM(quant, prob). Numeric. Returns the cumulative probability that the number of trials to obtain a success, when the probability of success is given by prob, will be less than or equal to quant.

CDF.HALFNRM. CDF.HALFNRM(quant, mean, stddev). Numeric. Returns the cumulative probability that a value from the half normal distribution, with specified mean and standard deviation, will be less than quant.

CDF.HYPER. CDF.HYPER(quant, total, sample, hits). Numeric. Returns the cumulative probability that the number of objects with a specified characteristic, when sample objects are randomly selected from a universe of size total in which hits have the specified characteristic, will be less than or equal to quant.

CDF.IGAUSS. CDF.IGAUSS(quant, loc, scale). Numeric. Returns the cumulative probability that a value from the inverse Gaussian distribution, with the given location and scale parameters, will be less than quant.

CDF.LAPLACE. CDF.LAPLACE(quant, mean, scale). Numeric. Returns the cumulative probability that a value from the Laplace distribution, with the specified mean and scale parameters, will be less than quant.

CDF.LNORMAL. CDF.LNORMAL(quant, a, b). Numeric. Returns the cumulative probability that a value from the log-normal distribution, with the specified parameters, will be less than quant.

CDF.LOGISTIC. CDF.LOGISTIC(quant, mean, scale). Numeric. Returns the cumulative probability that a value from the logistic distribution, with the specified mean and scale parameters, will be less than quant.

CDF.NEGBIN. CDF.NEGBIN(quant, thresh, prob). Numeric. Returns the cumulative probability that the number of trials to obtain a success, when the threshold parameter is thresh and the probability of success is given by prob, will be less than or equal to quant.

CDF.NORMAL. CDF.NORMAL(quant, mean, stddev). Numeric. Returns the cumulative probability that a value from the normal distribution, with specified mean and standard deviation, will be less than quant.

CDF.PARETO. CDF.PARETO(quant, threshold, shape). Numeric. Returns the cumulative probability that a value from the Pareto distribution, with the specified threshold and shape parameters, will be less than quant.

CDF.POISSON. CDF.POISSON(quant, mean). Numeric. Returns the cumulative probability that a value from the Poisson distribution, with the specified mean or rate parameter, will be less than or equal to quant.

CDF.SMOD. CDF.SMOD(quant, a, b). Numeric. Returns the cumulative probability that a value from the Studentized maximum modulus, with the specified parameters, will be less than quant.

CDF.SRANGE. CDF.SRANGE(quant, a, b). Numeric. Returns the cumulative probability that a value from the Studentized range statistic, with the specified parameters, will be less than quant.

CDF.T. CDF.T(M,S). Numeric and same as TCDF. Cumulative t distribution function of elements. Takes two arguments, a matrix of t values and a scalar giving the degrees of freedom (which must be positive). Returns a matrix having the same dimensions as M, containing the values of the cumulative t distribution function for each of its elements. If an element of the first argument is x and the second argument is S, then the corresponding element of the result is a number between 0 and 1, giving the proportion of a t distribution with S degrees of freedom that is less than x.

CDF.UNIFORM. CDF.UNIFORM(quant, min, max). Numeric. Returns the cumulative probability that a value from the uniform distribution, with the specified minimum and maximum, will be less than quant.

CDF.WEIBULL. CDF.WEIBULL(quant, a, b). Numeric. Returns the cumulative probability that a value from the Weibull distribution, with the specified parameters, will be less than quant.

CDFNORM(M). Standard normal cumulative distribution function of elements. Takes a single argument. Returns a matrix having the same dimensions as the argument, containing the values of the cumulative normal distribution function for each of its elements. If an element of the argument is x, the corresponding element of the result is a number between 0 and 1, giving the proportion of a normal distribution that is less than x. For example, CDFNORM({-1.96,0,1.96}) results in, approximately, {.025,.5,.975}.

CHICDF. CHICDF(M,S). Numeric and same as CDF.CHISQ. Chi-square cumulative distribution function of elements. Takes two arguments, a matrix of chi-square values and a scalar giving the degrees of freedom (which must be positive). Returns a matrix having the same dimensions as the first argument, containing the values of the cumulative chi-square distribution function for each of its elements. If an element of the first argument is x and the second argument is S, the corresponding element of the result is a number between 0 and 1, giving the proportion of a chi-square distribution with S degrees of freedom that is less than x. If x is not positive, the result is 0.

FCDF. FCDF(M,S1,S2). Numeric and same as CDF.F. Cumulative F distribution function of elements. Takes three arguments, a matrix of F values and two scalars giving the degrees of freedom (which must be positive). Returns a matrix having the same dimensions as the first argument M, containing the values of the cumulative F distribution function for each of its elements. If an element of the first argument is x and the second and third arguments are S1 and S2, the corresponding element of the result is a number between 0 and 1, giving the proportion of an F distribution with S1 and S2 degrees of freedom that is less than x. If x is not positive, the result is 0.

NCDF.BETA. NCDF.BETA(quant, shape1, shape2, nc). Numeric. Returns the cumulative probability that a value from the noncentral Beta distribution, with the given shape and noncentrality parameters, will be less than quant.

NCDF.CHISQ. NCDF.CHISQ(quant, df, nc). Numeric. Returns the cumulative probability that a value from the noncentral chi-square distribution, with df degrees of freedom and the specified noncentrality parameter, will be less than quant.

NCDF.F. NCDF.F(quant, df1, df2, nc). Numeric. Returns the cumulative probability that a value from the noncentral F distribution, with degrees of freedom df1 and df2, and noncentrality nc, will be less than quant.

NCDF.T. NCDF.T(quant, df, nc). Numeric. Returns the cumulative probability that a value from the noncentral Student's t distribution, with the specified degrees of freedom df and noncentrality nc, will be less than quant.

TCDF. TCDF(M,S). Numeric and same as CDF.T. Cumulative t distribution function of elements. Takes two arguments, a matrix of t values and a scalar giving the degrees of freedom (which must be positive). Returns a matrix having the same dimensions as M, containing the values of the cumulative t distribution function for each of its elements. If an element of the first argument is x and the second argument is S, then the corresponding element of the result is a number between 0 and 1, giving the proportion of a t distribution with S degrees of freedom that is less than x.