The growing interest in thermal comfort of outdoor environments yields in different analysis on courtyards as a common space between urban and architectural scales. However, there is a limited knowledge regarding the microclimatic behavior of such spaces. Using ENVI-met simulations, this paper aims to numerically discuss the thermal performance of different configurations of traditionally designed courtyards in Shiraz, Iran, which experiences hot summers and cold winters. The geometrical effects such as orientation and H/W (height to width ratio) of courtyards are considered as potential parameters to improve the microclimatic conditions. In this paper, PMV and UTCI are used as thermal comfort indices.The obtained results indicate mean radiant temperature and wind speed as the most effective parameters for thermal comfort of courtyards. In addition, the aforementioned geometrical parameters might not be able to solely create a desirable condition, but they could significantly improve the thermal comfort of courtyards during summer and winter. To achieve a desirable thermal comfort level, the results suggest using configurations of a high H/W rate and southward orientation in order to obtain better shading during summer as well as allowing the solar radiation in while regulating the wind speed in winter.

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In this paper, we propose a new transformation of circular random variables based on circular distribution functions, which we shall call inverse distribution function (id f) transformation. We show that Möbius transformation is a special case of our id f transformation. Very general results are provided for the properties of the proposed family of id f transformations, including their trigonometric moments, maximum entropy, random variate generation, finite mixture and modality properties. In particular, we shall focus our attention on a subfamily of the general family when id f transformation is based on the cardioid circular distribution function. Modality and shape properties are investigated for this subfamily. In addition, we obtain further statistical properties for the resulting distribution by applying the id f transformation to a random variable following a von Mises distribution. In fact, we shall introduce the Cardioid-von Mises (CvM) distribution and estimate its parameters by the maximum likelihood method. Finally, an application of CvM family and its inferential methods are illustrated using a real data set containing times of gun crimes in Pittsburgh, Pennsylvania.

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