The sample copula of order $m$ provides an approximation to the copula that characterizes the dependence structure of a set of random variables. In this work, we first derive the sample copula of order $m$ for a random vector $X = (X_{1},\ldots ,X_{d})$ , with $d \geq 2$ , by extending previously established results for the bivariate case. Based on the definition of a parametric copula with piecewise constant density, we show that the maximum likelihood estimation of the density parameters coincides with the elements employed in the definition of the sample copula of order $m$ , under the condition $2 \le m \le n$ , where $m$ is an integer divisor of $n$ , and $n$ denotes the given sample size. In the second part, we present an application of the sample copula of order $m$ as a complementary alternative for estimating the cosmological parameters $H_{0}$ and $\Omega _{m0}$ , the current values of the Hubble constant and the matter density, respectively. This is carried out using a sample of observations of the redshift $z$ , the Hubble parameter $H$ , and its measurement error. To this end, several probability distributions, in addition to the Gaussian distribution, are proposed to model the observed error in the variable $H$ . Moreover, the applicability of this methodology is highlighted in the context of limited sample sizes.
