Inverse Length Biased Maxwell Distribution:Statistical Inference with an Application

In this paper,we suggested and studied the inverse length biased Maxell distribution(ILBMD)as a new continuous distribution of one parameter.The ILBMD is obtained by considering the inverse transformation technique of the Maxwell length biased distribution.Statistical characteristics of the ILBMD such as the moments,moment generating function,mode,quantile function,the coefficient of variation,coefficient of skewness,Moors and Bowley measures of kurtosis and skewness,stochastic ordering,stress-strength reliability,and mean deviations are obtained.In addition,the Bonferroni and Lorenz curves,Gini index,the reliability function,the hazard rate function,the reverse hazard rate function,the odds function,and the distributions of order statistics for the ILBMD,are presented.The ILBMD parameter is estimated using the maximum likelihood method,the method of moments,the maximum product of spacing technique,the ordinary and weight least square procedures,and the Cramer-Von-Mises methods.The Fishers information,as well as the Rényi and q-entropies,are derived.To investigate the usefulness of the proposed lifetime distribution and to illustrate the purpose of the study,a real dataset of the relief times of 20 patients receiving an analgesic is used.

Chromosome organization and gene expansion in the highly fragmented genome of the ciliate Strombidium stylifer

Chromosomes are well-organized carriers of genetic information in eukaryotes and are usually quite long,carrying hundreds and thousands of genes.Intriguingly,a clade of single-celled ciliates,Spirotrichea,feature nanochromosomes—also called“gene-sized chromosomes”.These chromosomes predominantly carry only one gene,flanked by short telomere sequences.However,the organization and copy number variation of the chromosomes in these highly fragmented genomes remain unexplored in many groups of Spirotrichea,including the marine Strombidium.Using deep genome sequencing,we assembled the macronuclear genome of Strombidium stylifer into more than 18,000 nanochromosomes(~2.4 Kb long on average).Our results show that S.stylifer occupies an intermediate position during the evolutionary history of Strombidium lineage and experienced significant expansions in several gene families related to guanyl ribonucleotide binding.Based on the nucleotide distribution bias analysis and conserved motifs search in non-genic regions,we found that the subtelomeric regions have a conserved adenine-thymine(AT)-rich sequence motif.We also found that the copy number of nanochromosomes lacks precise regulation.This work sheds light on the unique features of chromosome structure in eukaryotes with highly fragmented genomes and reveals that a rather specialized evolutionary strategy at the genomic level has resulted in great diversity within the ciliated lineages.