MPS: An R package for modelling shifted families of distributions

Abstract

Generalised statistical distributions have been widely used over the last decades for modelling phenomena in different fields. The generalisations have been made to produce distributions with more flexibility and lead to more accurate modelling in practice. Statistical analysis of the generalised distributions requires new statistical packages. The Newdistns package due to Nadarajah and Rocha provides R routines with functionality to compute probability density function (PDF), cumulative distribution function (CDF), quantile function, random numbers and parameter estimates of 19 families of distributions with applications in survival analysis. Here, we introduce an R package, called MPS, for computing PDF, CDF, quantile function, random numbers, Q-Q plots and parameter estimates for 24 shifted new families of distributions. By considering an extra location parameter, each family will be defined on the whole real line and so covers a broader range of applicability. We adopt the well-known maximum product spacing approach to estimate parameters of the families because under some situations the maximum likelihood (ML) estimators fail to exist. We demonstrate MPS by analysing two well-known real data sets. For the first data set, the ML estimators break down, but MPS works well. For the second set, adding a location parameter results in a reasonable model while the absence of the location parameter makes the model quite inappropriate. The MPS is available from CRAN at https://cran.r-project.org/package=MPS.

On the study of the stress-strength reliability in Weibull-$F$ Models

“…It would appear that W(1.1978,0.0738, 1 − e −0.0103x ) and W(1.1392,0.0624,1 − e −0.0117y ) are totally good to fit data set I and data set II, respectively. For computing the p-value, we applied the command mpsweibullextg(...) in MPS R Package [23]. In this package, the significance level for the aforementioned goodness-of-fit test is reported.…”

Bayesian Estimation Using Product of Spacing for Modified Kies Exponential Progressively Censored Data

“…where we choose to use the gamma prior due to its mathematical flexibility and ability to cover a wide range of prior beliefs held by the experimenter; for more details, see Fathi et al [24], Eliwa et al [25], and Dey et al [26]. By combining the LF in (7) and the joint prior distribution (17), the joint posterior distribution is provided by…”

“…Singh et al [14] obtained the point and asymptotic interval estimations of the parameters of generalized inverted exponential distributions using the MPS, ML, and least squares methods. For more, see the works of Singh et al [6], Rahman et al [15], Aruna [16], Teimouri and Nadarajah [17], Almetwally et al [18], and Tashkandy et al [19].…”

Pan-cancer analysis reveals potential for synergy between SERPINA1 molecular targeting and macrophage-related immunotherapy

“…Multiple tumor immunological scores and SERPINA1 expression were mapped using a spearman correlation analysis. Different cancer types were represented by the horizontal axis, and different immune scores are represented by the vertical axis in heatmaps [32][33][34][35][36].…”

“…Multiple tumor immunological scores and SERPINA1 expression were mapped using a spearman correlation analysis. Different cancer types were represented by the horizontal axis, and different immune scores are represented by the vertical axis in heatmaps [32][33][34][35][36].2.8 Pan-Cancer Analysis of the Correlation of the SERPINA1 with Tumor Cell In ltration, Immune Modulator Genes, and Immune CheckPoint.The R package ESTIMATE was used to further calculate each patient's stromal, immune, and ESTIMATE scores for each tumor [37]. Moreover, the SERPINA1 gene and 60 immune checkpoint pathway genes were extracted [38], The Pearson correlation between SERPINA1 and the ve types of immune pathway marker…”