*3.1. DBSCAN*

The DBSCAN (density-based spatial clustering of applications with noise) [26] algorithm is the precursor of all density-based clustering algorithms. It was developed to process large datasets with the inherent presence of noise. DBSCAN is capable of discriminating the noise points of a dataset and can detect clusters of any shape with no previous information about the number of expected clusters. Shortly, DBSCAN leverages the concepts of *core points*, *density-reachability*, and *density-connectivity*. Given two parameters and *minPts*, a point is a *core point* if there are at least *minPts* points in its neighborhood of radius (-neighborhood). A point *p* is directly density-reachable from a point *q* if *q* is a core point and *p* is in *q*'s -neighborhood. Two points *p* and *q* are *density-reachable* if there exists a chain of directly density-reachable points that connect *q* and *p*. Finally, two points *p* and *q* are *density-connected* if there exists a core point *o* such that *p* and *q* are density-reachable from *o*.

DBSCAN builds a cluster of points by iteratively connecting a couple of points that are density-connected, and all the points that are density-reachable from a point of the cluster are in the same cluster. All points that do not belong to any cluster, and thus are not density-connected to any other point, are considered noise points. The DBSCAN can process a dataset of size *n* in *O*(*nlogn*) time if exploiting a proper indexing structure on the data for executing the search for the -neighborhood. It is worth noting that, given the definitions above, it is clear that DBSCAN can detect clusters having at least a specific predetermined density ( *minPts πr*2 ), directly determined by the and *minPts* parameters. For such a reason, it can fail to detect clusters characterized by different densities.


**Author details**

Heru Rahadyan Bank Indonesia, Jakarta, Indonesia

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© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Currency and Banking Crises: The Origins and How to Identify Them DOI: http://dx.doi.org/10.5772/intechopen.107245*


**7. Conclusions**

The article's major contribution is a flexible trigonometric extension of the well-known modified Lindley model that proposes a novel efficient statistical modelling technique. We employ the features of the sine generalized family of distributions in this regard, and develop the sine modified Lindley distribution. We have displayed a few of its more noteworthy attributes, with a focus on the shape properties of the corresponding probability density and hazard rate functions, as well as discussing moments. Simulation studies and applications demonstrate the utility of the model under consideration. In particular, we compared it to the primary current models derived from the Lindley, exponential and other models with one or more parameters, using two real-world data sets. As a result, the obtained findings are really satisfactory, demonstrating that the novel distribution has a wide range of applications that could be the subject of additional research in a variety of scientific fields.

**Author Contributions:** Conceptualization, L.T., V.G. and C.C.; methodology, L.T., V.G. and C.C.; software, L.T., V.G. and C.C.; validation, L.T., V.G. and C.C.; formal analysis, L.T., V.G. and C.C.; investigation, L.T., V.G. and C.C.; writing—original draft preparation, L.T., V.G. and C.C.; writing review and editing, L.T., V.G. and C.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** We would like to express our gratitude to the four reviewers for their useful comments on the work's first draft.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**1. Introduction**

Radon (Rn) is a colorless, odorless, tasteless, inert radioactive gas, and derives from the decay of uranium, which is a radioactive element that is found in small quantities in all sediments and rocks.

The International Agency for Research on Cancer (IARC) and the World Health Organization (WHO) classify Rn pollution as the second leading cause of lung cancer after smoking.

Since Rn is present, in the depths of the Earth, in gaseous phase, it reaches the surface because it interacts with other natural elements, such as uranium, thorium and radio (precursor elements); moreover other geo-lithological features, such as the mineralogical composition of the rocks, the underground permeability levels, the presence of faults, fractures and cavities, affect the transport of the Rn on the surface.

In this paper, the spatial distribution of the Rn concentrations in soil gas over a survey area located in the South of Apulian Region (Italy) and its prediction at unsampled points have been discussed. In particular, Ordinary Kriging (OK), Log-Normal Kriging (LK), Cokriging with indicator variable (ICK) and Kriging with Varying Means (KVM) [11, 21, 26, 27] have been used to predict Rn concentrations over the study area.

In this context, the integration of a Geographical Information System (GIS) and geostatistical tools can certainly support the evaluation of alternative scenarios, possible strategies for a sustainable development [1].

In addition, the geoprocessing tools (e.g., buffering, overlay, union/intersection, interpolation) can be used to combine and interpret data obtained from different sources. The construction of a GIS project facilitates the data sharing and the integration of environmental and demographic data, as well as the results of spatial analysis.

Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

©2012 Author(s), licensee InTech. This is an open access chapter distributed under the terms of the Creative

Thus, the usefulness of geostatistical techniques for monitoring Rn concentrations in soil gas and the integration of these results in an *ad hoc* WebGIS, named RnWebGIS, have been described. This innovative tool offers dynamic scenarios for monitoring and analyzing different environmental variables [7, 39]. The proposed RnWebGIS is based on an Open Source Software, which enables users to get online spatial and environmental information.

Hence, after a discussion on the integration of GIS and geostatistical tools (Section 2), a brief review of some geostatistical techniques for modeling and prediction purposes has been presented (Section 3). A thorough case study concerning the Rn concentration in soil gas measured in several sites over Lecce district has been developed (Section 4). Finally, the RnWebGIS, where all the available geo-lithological information of the area under study, as well as the Rn prediction results have been integrated, has been proposed and the steps for its implementation have been detailed.


2.3.1. Library Preparation

Purified genomic DNA from each sample was initially amplified in a 25 μL reaction, using the REDExtract-N-Amp PCR ReadyMix (Sigma-Aldrich, St Louis, MO, USA) with 0.4 μM of each 16S rRNA gene primer and 2 μL template. The 16S PCR conditions were the following: an initial denaturation at 95 ◦C for 2 min, 20 cycles of 95 ◦C for 30 s, 60 ◦C for 1 min and 72 ◦C for 30 s and final elongation at 72 ◦C for 7 min. This PCR run is referred to as PCR1. The product from PCR1 was prepared for sequencing by a second PCR (referred to as PCR2), using the same PCR protocol as described above. PCR2 attached an adaptor A, an index i5 and a forward sequencing primer site (FSP) in the 5' end of the amplicons and an adaptor B, an index i7 and a reverse sequencing primer site (RSP) to the 3' end of the amplicons. DNA was quantified using the Quant-ITTM dsDNA High Sensitive Assay Kit (Thermo Fisher Scientific, Waltham, MA, USA) and PCR2 products were pooled in equimolar amounts between samples. Agencourt AMPure XP bead (Beckman Coulter, Brea, CA, USA) purification was performed to remove undesirable DNA amplicons from the pooled amplicon library (PAL) in a two-step process. First, DNA fragments below 300 nucleotides length were removed by a PAL AMPure beads 10:24 ratio, following the manufacturer's instructions, and eluted in 40 μL TE bu ffer (AM1). Secondly, large DNA fragments above 1kbp were removed by AM1 to AMPure beads 10:16 ratio as previously described. The resulting AMPure beads purified PAL (bPAL) was diluted to a final concentration of 11.5 pM DNA in a 0.001 N NaOH and used for sequencing on the Illumina MiSeq desktop sequencer (Illumina Inc., San Diego, CA, USA). The library was sequenced with the 500-cycle MiSeq Reagent Kit V2 in a 2 × 250 nt setup (Illumina Inc., San Diego, CA, USA). The sequencing was performed at Statens Serum Institute (SSI).