Abstract The first-order two-state Markov chains have been used for modelling daily sunshine duration and global solar radiation data, recorded in Reading (United Kingdom), Kuwait-City (Kuwait) and various locations in Algeria (i.e., Algiers, Batna, Oran and Setif) during periods of 8–21 years. In a different way, these data were represented by a model based on the observation of two independent states, called “bad weather” and “fine weather”, respectively. In comparing both models, similarities are, respectively, found between the long-term Markovian and a priori probabilities of having one of both states, the Markovian and arithmetical computations of the mean, the one-day lag autocorrelation and persistence coefficients. The identity between the long-term Markovian and a priori probabilities means that the steady state of the first-order two-state Markov process is described by a Bernoulli random variable. If the identities mentioned above are proved for other locations in the world, they could supplement the statistical tests of validity of this type of Markov models. For instance, it is shown that the properties involved by the limiting distribution of first-order two-state Markov chains, are useful for sizing stand-alone photovoltaic systems in Algiers and for analyzing their performances.