Modelling ground-level ozone concentration using copulas

Many random variables occurring in nature are circular random variables, i.e., its probability density function has period 2 pi and its support is the unit circle. The support of a linear random variable is a subset of the real line. When one is interested in the relation between a circular random variable and a linear random variable it is necessary to construct their joint distribution. The support of the joint distribution of a circular and a linear random variable is a cylinder. In this paper, we use copulas and circular distributions based on non-negative trigonometric sums to construct the joint distribution of a circular and a linear random variable. As an application of the proposed methodology the hourly quantile curves of ground-level ozone concentration for a monitoring station in Mexico City are analyzed. In this case the circular random variable has a uniform distribution if we have the same number of observations in each hour during the day and, the linear random variable is the ground-level ozone concentration.