In basic probability courses, addressing the issue of random vectors shows that the marginal distributions of such vectors can be obtained in a unique way from the joint distribution. The reciprocal of this affirmation does not necessarily have. This article of informative type, tries, by means of a counterexample taken from Embrechts et al. (2002), and that makes use of the theory of copulas, to illustrate the fallacy: “ Marginal distributions and correlation determine the joint distribution ”.Keywords: correlation coefficient; joint distribution; marginal distribution; bivariate normal distribution; copulation theory; random vectors.

On march 6 of 2020, the first case of COVID-19 was reported in Colombia. This virus, declared a public health emergency of international importance, has affected different sectors. There is a boom in the number of studies that make forecasts in various aspects that have to do with this virus. The present work shows the theoretical aspects of recurrent neuronal networks and his use to create a 60-day forecast on cumulative cases, cumulative deaths and cumulative recovered, available from march 6 2020 to march 6 2022. Neural networks with GRU and LSTM cells along with the classic RNN were used to make these forecasts.

Diversas distribuciones generalizadas se desarrollan en la literatura estadística, entre ellas se encuentra la distribución Secante Hiperbólica Generalizada (SHG). En este documento se presenta un método alternativo para la estimación de los parámetros poblacionales de la SHG, llamado Máxima Verosimilitud Modificada (MVM). Asumiendo algunas expresiones alternas que difieren con el trabajo de Vaughan en el 2002 y basándose en el mismo conjunto de datos de la fuente original. Se implementa computacionalmente el método transformado de MVM, permitiendo observar unas buenas aproximaciones de los valores de los parámetros de localización y escala, presentados por Vaughan en su artículo. Con esto se pretende que en la práctica se cuente con una metodología diferente para estimar. MSC: 60E05, 62E10

The Generalized Lambda Distribution (GLD) is a four-parameter distribution defined by a percentile function. Its functional form allows to model different data sets and a wide range of distributions. The four parameters estimation may be carried out through different methods such as: moments method, least squares method, maximum likelihood method, among others. This paper wants to describe the method for estimating the distribution of interest, called the Method of Percentiles. An illustration is shown, fitting the distribution to data sets well approximate to a particular theoretical distribution.

Panjer’s algorithm used in the calculation actuarial basis taking class distributions (a,b), presents a recursive formula for calculating function distribution of sums of random variables in a model of collective risk. If the secondary distribution in this model is the ETNBD, Compound Poisson distribution is named PoissonPascal, this is a family of distributions very used in the mathematics of insurance and can generate models statistically appropriate. It illustrates the methodology application to a data set of a portfolio of policies cars, in addition the algorithm is implemented using the statistical software R.

For insurance companies the reservation process is the fundamental basis for controlling portfolios contracted to facilitate the manipulation of mathematical and probabilistic model. Sometimes the model is discretized so that the results approximate the real solution in the continuum, in this case the compound binomial model is used for this purpose. In most contexts the assumption of independence is assumed, in this article we consider dependence between two types of complaints referred to the principal claim and over-claim or subsequent claim, the latter will be involved whenever there is a claim principal. The type of model with timerelated claims process generates two reserves, one for when the subsequent claim is not delayed to a next time and another where it covers the total claimed by both the principal and by the subsequent claim. Since manipulate these processes separately is unnecessary and impractical, we generate from the survival probabilities of both processes and manipulate the probability generating functions, an equation that collects information from the two processes of reserves.