## 1 Introduction  
Ionizing radiation exposure, both for the general public and for specialists, is a cutting-edge research topic. Ionizing radiation can originate from both natural and man-made sources [1, 2]. In particular, the radiation of natural origin (understood as background radiation), includes three main components: (_i_) cosmic rays [3]; (_ii_) cosmogenic radioisotopes; (_iii_) and primordial radioisotopes [4]. The majority of natural radioactivity is due to a terrestrial component created by primordial radionuclides that produce three decay series: \({}^{238}\)U, \({}^{235}\)U, and \({}^{232}\)Th. Each of these decay series produces radon isotopes. The \({}^{222}\)Rn isotope and its decay products are the most abundant source of natural ionizing radiation, accounting for the vast majority of the effective dose to human life. Epidemiological studies have discovered a relationship between radon concentration exposure and the risk of lung cancer [5; 6; 7; 8]. Dense radon concentration maps are required to execute successful locally based risk reduction efforts, with geostatistical interpolation approaches possibly inferring the expected concentration when fewer data are available. The Council Directive 2013/59/Euratom [9], which Italy enacted in July 2020 (Legislative Decree 101/2020), was the first control for radon exposure in homes in the European Union. As a result, Member States must promote public awareness about indoor radon danger. According to the literature, soil is the major source of radon. In this context, it is believed that the radon concentrations following the geological map are spatially linked and give rise to stationary distributions, at least over restricted areas. Indoor concentration measurements, in contrast, are impacted by a number of factors and hence display significant fluctuation, resulting in spatially non-stationary distributions of values. As a result, applying interpolation techniques based on variogram calculation, such as kriging, can be difficult because these techniques must be implemented using advanced fits (such as nested structures) or after data preprocessing [10]. To address these constraints, several writers devised a new technique based on the calculation of the Gini index, a tool typically employed in the socio-economic sector for income distribution studies but with applicability in a wide range of disciplines [11; 12]. Indoor radon measurements in Sorrentina peninsula homes were conducted voluntarily by families that attended a scientific presentation [13]. Individuals spend most of their time at home, i.e., at least 30% of the day. In this investigation, roughly 70 houses (measurement locations) were employed to evaluate the spatial distribution of the yearly average concentration of Rn. This sample size is adequate for creating indoor Rn maps of the predicted average concentration in the Sorrentina peninsula area using geostatistical methods. To ensure the radon measurements were independent of the floor on which they were obtained, the first step was to normalize the data with respect to the ground floor. The Gini index was used to create the interpolated maps for this case study [12; 13; 14]. This index is bounded above because it can only take on a value of one, implying that it may make detecting quasi-stationarity distributions more difficult. In such instances, computing the classical semi-variogram may be required to confirm the quasi-stationarity. The Gini index distinguishes fluctuations caused by environmental factors from those caused by random spatially uncorrelated noise, and also allows a better constraint of the critical distance below which the radon geological source can be considered to be uniform, at least for the length scales of variability studied. In the sections that follow, we first provide a brief review of the literature on the methodologies used to map radon distribution in the State of the Art section (Section 2).