On the analysis of power law distribution in software component sizes

Abstract

Component-based software development (CBSD) is an active area of research. Ascertaining the quality of components is important for overall software quality assurance in CBSD. One of the important metrics for measuring defects, analyzability, efforts, and cost in CBSD is component size. The paper presents an analytical model based on maximization of Tsallis entropy to obtain closed form expression for component size distribution (maximum Tsallis entropy component size distribution, MTECSD) in steady state. It is found that the component size distribution follows power law asymptotically. A procedure based on generalized Jensen-Shannon measure is developed to estimate model parameters. A detailed analysis of many popular probability distributions along with MTECSD is carried out on many diverse real data sets of component-based softwares. The analysis reveals that lognormal and MTECSD distributions fit well to component sizes in many software conforming the presence of power law behavior. The software whose component size distributions are described by MTECSD are in equilibrium implying that new defects in these software systems occur occasionally. Power law behavior in component sizes also imply high variation leading to difficulty in software analyzability. The precise knowledge of component size distribution also provides an alternative method to compute efforts and cost estimates by modified COCOMO model.

Some Properties of Zipf’s Law and Applications

“…The most prolific research direction regarding Zipf's law has been the applicative one: finding applications verifying the laws with a reasonable approximation and the range of parameters that determine a good fit. Application domains comprise linguistics [5][6][7], medicine [8,9], arts [10,11], computer science [12,13], communications [14], signal processing [15][16][17], economics [4], including firm growth and death [18,19], demography [1,20], patents [21,22], tourism [23], and speech [24].…”

Gaining insights in datasets in the shade of “garbage in, garbage out” rationale: Feature space distribution fitting

“…The example phenomena reflecting these distributions are compiled and categorized from (Limpert et al, 2001; Milojević, 2010; Newman, 2004; White et al, 2008) or other resources with given references as follows: Natural phenomena fitting log‐normal : element concentration in the Earth's crust, latent periods (from infection to the first symptoms) of infectious disease [e.g., the incubation period of Coronavirus disease 2019 (COVID‐19), SARS (severe acute respiratory syndrome), and MERS (Middle East Respiratory Syndrome; Backer et al, 2020)], the abundance of bacteria on plants; Unnatural phenomena fitting log‐normal : number of letters per word, number of words per sentence, age of first marriage in Western; Natural phenomena fitting exponential : damage in nuclear power incidents and accidents before 1980 (Wheatley et al, 2017), moderate‐sized disasters (observed sea‐level variations, wind velocity, annual river floods) (Pisarenko & Rodkin, 2010), the arrival rate of cosmic ray alpha particles or Geiger counter tics (Tobias, 2012); Unnatural phenomena fitting exponential : time to failure patterns (also in natural phenomena) (Frank, 2009), modeling malware propagation delays (Wang & Murynets, 2013), frequency of Korean family names (power law in family names in the world), intervals between aircraft arrivals to major airports (Willemain et al, 2004), the inter‐arrival times of the 911 calls (Albert, 2011), the time between goals in World Cup football matches (Chu, 2003), the dispersion of U.S. incomes which was qualified as a kind of thermal equilibrium (Bartels, 2012); Natural phenomena fitting power law : island sizes, lake sizes, flood magnitudes, species body sizes, individual body sizes (White et al, 2008), basic community structure descriptors (number of species, links, and links per species) with the area (Galiana et al, 2022); and Unnatural phenomena fitting power law : author productivity, citations received by papers, scattering of scientific literature (Milojević, 2010). Component sizes in component‐based software development (Sharma & Pendharkar, 2022). The above phenomena are provided to introduce the statistical distributions by examples revealing their diversities and to allow the researchers to relate them to the distributions observed in their datasets.…”