Package PredictionR. October 6, Index 7. Best fitting of a distribution to a data

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1 Package PredictioR October 6, 2018 Title Predictio for Future Data from ay Cotiuous Distributio Versio Author H. M. Barakat [aut], O. M. Khaled [aut], Hadeer A. Ghoem [aut, cre] Maitaier Hadeer A. Ghoem Descriptio Fuctios to get predictio itervals ad predictio poits of future observatios from ay cotiuous distributio. Licese GPL (>= 2) LazyData TRUE Imports stats, fitdistrplus Suggests actuar NeedsCompilatio o Repository CRAN Date/Publicatio :30:14 UTC R topics documeted: bestfit predi predp Idex 7 bestfit Best fittig of a distributio to a Descriptio Fit of a distributio to a by two methods: maximum likelihood (mle) ad momet matchig (mme). Kolmogorov-Smirov test is used to costruct the best fittig. 1

2 2 bestfit Usage bestfit(, dist, order=null, start=null, cof=0.95) Argumets dist order start cof A umeric vector A character strig "ame" amig a distributio for which the correspodig desity fuctio dame, the correspodig distributio fuctio pame ad the correspodig quatile fuctio qame must be defied. A umeric vector for the momet order(s). The legth of this vector must be equal to the umber of parameters to estimate. This argumet may be omitted(default) for some distributios for which reasoable order are computed. A amed list givig the iitial values of parameters of the amed distributio. This argumet may be omitted(default) for some distributios for which reasoable startig values are computed. Cofidece level for the test. Details This fuctio is ot iteded to be called directly but is iterally called i predi ad predp. It is assumed that the two methods: "mle" ad "mme" are applied the Kolmogorov-Smirov test is used to costruct the best fittig. Value bestfit returs a list with followig compoets, fit p.value the parameter estimates. the pvalue of the Kolmogorov-Smirov Test. Author(s) H. M. Barakat, O. M. Khaled ad Hadeer A. Ghoem. Refereces Deligette-Muller ML ad Dutag C (2015), fitdistrplus: A R Package for Fittig Distributios. Joural of Statistical Software, 64(4), See Also predi, predp.

3 predi 3 Examples best fittig of a logistic distributio =100 x1 <- rlogis(, 0.5, 0.8) bestfit(x1, "logis") bestfit(x1, "logis")$p.value predi Predictio iterval for future observatios Descriptio Costruct a predictio iterval (PCI) for future observatios from ay cotiuous distributio. Geeric method is prit. Usage predi(, dist, s,, order=null, start=null, cof=0.95) S3 method for class 'predi' prit(x,...) Argumets dist s order start cof x A umeric vector A character strig "ame" amig a distributio for which the correspodig desity fuctio dame, the correspodig distributio fuctio pame ad the correspodig quatile fuctio qame must be defied. A umeric vector for the order of the ext observatio. The legth of this vector must be equal to 1. A umeric vector for the size of all. A umeric vector for the momet order(s). The legth of this vector must be equal to the umber of parameters to estimate. This argumet may be omitted(default) for some distributios for which reasoable order are computed. A amed list givig the iitial values of parameters of the amed distributio. This argumet may be omitted(default) for some distributios for which reasoable startig values are computed. Cofidece level for the test. A object of class "predi".... Further argumet to be passed to geeric fuctio

4 4 predi Details Value The dist argumet is assumed to specify the distributio by the probability desity fuctio, the commulative distributio fuctio ad the quatile fuctio (d, p, q). By default, best fittig of the based o maximum likelihood (mle) ad momet matchig (mme) methods is performed. oce the parameter(s) is(are) estimated, predi computes the predictio iterval (PCI) for the future observatio. This fuctio will be called directly i predp. predi returs a object of class "predi", a list with the followig compoets: iterval lower upper distame r s parameters the predictio iterval. the lower boud of the iterval. the upper boud of the iterval. the ame of the distributio. the legth of the. the order of the ext observatio. the legth of all the. the parameter estimate. Geeric fuctio: prit The prit of a "predi" object shows few traces about the parameters ad the predictio iterval. Author(s) H. M. Barakat, O. M. Khaled ad Hadeer A. Ghoem. Refereces Deligette-Muller ML ad Dutag C (2015), fitdistrplus: A R Package for Fittig Distributios. Joural of Statistical Software, 64(4), H. M. Barakat, Magdy E. El-Adll, Amay E. Aly (2014), Predictio itervals of future observatios for a sample radom size from ay cotiuous distributio. Mathematics ad Computers i Simulatio, volume 97, See Also bestfit, predp. Examples (1) predictio iterval for the ext observatios based o ormal distributio set.seed(123) x1 <- rorm(15, 2, 4) predi(x1, "orm", 16, 25)

5 predp 5 (2) predictio iterval for the ext observatios based o weibull distributio library(actuar) set.seed(123) x2 <- rweibull(16, 2, 3) predi(x2, "weibull", 20, 20 ) predp Predictio poit for future observatios Descriptio Costruct a predictio poit for future observatios from ay cotiuous distributio. method is prit. Geeric Usage predp(, dist, o,, order=null, start=null, cof=0.95) S3 method for class 'predp' prit(x,...) Argumets dist o order start cof x A umeric vector A character strig "ame" amig a distributio for which the correspodig desity fuctio dame, the correspodig distributio fuctio pame ad the correspodig quatile fuctio qame must be defied. A umeric vector for the umber of the ext observatios. The legth of this vector plus the legth of the must be less tha or equal the legth of all. A umeric vector for the size of all. A umeric vector for the momet order(s). The legth of this vector must be equal to the umber of parameters to estimate. This argumet may be omitted(default) for some distributios for which reasoable order are computed. A amed list givig the iitial values of parameters of the amed distributio. This argumet may be omitted(default) for some distributios for which reasoable startig values are computed. Cofidece level for the test. A object of class "predi".... Further argumet to be passed to geeric fuctio

6 6 predp Details Value By default, best fittig of the based o maximum likelihood (mle) ad momet matchig (mme) methods is performed. oce the parameter(s) is(are) estimated, predp computes the predictio poit(s) for the future observatio(s). predp returs a object of class "predp", a list with the followig compoets: ewobs s o distame ld the ew with ew observatios. the ew observatios. the rak of the ew observatios. the umber of the ext observatios. the ame of the distributio. the legth of the. the legth of all the. Geeric fuctio: prit The prit of a "predp" object shows the predictio poit(s) for the future observatio(s). Author(s) H. M. Barakat, O. M. Khaled ad Hadeer A. Ghoem. Refereces Deligette-Muller ML ad Dutag C (2015), fitdistrplus: A R Package for Fittig Distributios. Joural of Statistical Software, 64(4), H. M. Barakat, Magdy E. El-Adll, Amay E. Aly (2014), Predictio itervals of future observatios for a sample radom size from ay cotiuous distributio. Mathematics ad Computers i Simulatio, volume 97, H. M. Barakat, O. M. Khaled ad Hadeer A. ghoem (2018), Predictig future lifetime based o radom umber for mixture expoetial distributio. Iteratioal coferece of mathematics ad its applicatios (ICMA18), April, 2018, Cairo, Egypt. See Also bestfit, predi. Examples predictio poit for the ext observatios based o gamma distributio set.seed(123) x1 <- rgamma(10, 4, 2) predp(x1, "gamma", 8, 20)

7 Idex bestfit, 1, 4, 6 predi, 2, 3, 6 predp, 2, 4, 5 prit.predi (predi), 3 prit.predp (predp), 5 7

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