ensembl-nov2015

data for Fig.1: ensembl-nov2015.txt column 1: Ensembl gene family ID column 2: number of genes in the (Ensembl) gene family column 3: description of the (Ensembl) gene famil

gene-fam-with-TF

data for Fig.4: gene-fam-with-TF.txt column 1: HGNC gene family ID or name column 2: number of transcription factors in the (HGNC) gene family column 3: number of genes in the (HGNC) gene family (possibly including pseudogenes) column 4: description of the (HGNC) gene famil

gf-size-feb2016

data for Fig.2: gf-size-feb2016.txt column 1: HGNC gene family ID or name column 2: number of genes in the (HGNC) gene family (possibly including pseudogenes) column 3: number of genes in the (HGNC) gene family (excluding pseudogenes) column 4: description of the (HGNC) gene famil

gene-fam-with-drug-target

data for Fig.5: gene-fam-with-drug-target.txt column 1: HGNC gene family ID or name column 2: number of drug target genes (gene products) in the (HGNC) gene family column 3: number of genes in the (HGNC) gene family (possibly including pseudogenes) column 4: description of the (HGNC) gene famil

DGBD fits for various distributions.

<p>The estimated <i>a</i> and <i>b</i> parameter values in DGBD (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0163241#pone.0163241.e001" target="_blank">Eq (1)</a>) for data generated by well known distributions. Size of the dots indicate the coefficient of determination R squared. The dots around the <i>a</i> = <i>b</i> diagonal line are for data generated by the lognormal distribution.</p

Pdf of the Lavalette distribution.

<p>Some Lavalette probability density functions (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0163241#pone.0163241.e006" target="_blank">Eq (4)</a>) with identical parameter <i>C</i> = 1 but with a = 1/5, 1/3, 1, 2, 3, and 4 (<i>m</i> = 1/<i>a</i> = 1/<i>b</i>).</p

Beyond Zipf’s Law: The Lavalette Rank Function and Its Properties

<div><p>Although Zipf’s law is widespread in natural and social data, one often encounters situations where one or both ends of the ranked data deviate from the power-law function. Previously we proposed the Beta rank function to improve the fitting of data which does not follow a perfect Zipf’s law. Here we show that when the two parameters in the Beta rank function have the same value, the Lavalette rank function, the probability density function can be derived analytically. We also show both computationally and analytically that Lavalette distribution is approximately equal, though not identical, to the lognormal distribution. We illustrate the utility of Lavalette rank function in several datasets. We also address three analysis issues on the statistical testing of Lavalette fitting function, comparison between Zipf’s law and lognormal distribution through Lavalette function, and comparison between lognormal distribution and Lavalette distribution.</p></div

Lognormal vs Lavalette cdf.

<p>Cumulative distribution function for lognormal and Lavalette distributions, being <i>μ</i> = 0 and <i>σ</i> = 0.1, 0.5 and 1 the parameters of the lognormal. The <i>x</i> axis is in logarithmic scale. We see that over an important interval of the domain, it may be difficult to distinguish a lognormal from a Lavalette distribution.</p

Ranked datasets fitted by Lavalette rank function.

<p>(A) Nigeria (NRG) local government area (the secondary administrative unit (SAU)) population; (B) Madrid and Cádiz municipality (the tertiary administrative unit (TAU)) population; (C) Amino acid to amino acid mutation counts in the 1000 Genomes Project; (D) Averaged codon usage (excluding the three stop codons) of plant organelles and mammals.</p