# Need some help to identify the appropriate distribution

The residual plots of the following models are not normal, while the distribution of residuals between (-3 to 3) is normal in model m17. The worm plot of all equations appears to be correct. The goal of this project is to calculate the reference equation using the LMS approach. 1. Could you please tell me if the BCCGo distribution is adequate for this data? If not, which family would you suggest? > 2. Which of these equations performs the best? Why? Thanks so much for your time and help in advance.

m4 <- gamlss(y ~ log(Ph1_Groesse) + pb(log(Ph1_Alter_2)), sigma.fo =~pb(log(Ph1_Alter_2)), nu.fo=~log(Ph1_Alter_2), family = BCCGo(mu.link = "log"), data=DAT1.F)

m17 <- gamlss(y ~ log(Ph1_Groesse) + pb(Ph1_Alter_2), sigma.fo =~pb(Ph1_Alter_2), nu.fo =~pb(Ph1_Alter_2), family = BCCGo(mu.link = "log"), data=DAT1.F)

m24 <- gamlss(y ~ log(Ph1_Groesse) + pb(log(Ph1_Alter_2)), sigma.fo =~pb(log(Ph1_Alter_2)), nu.fo=~log(Ph1_Alter_2), tau.fo=~log(Ph1_Alter_2), family = BCPE(mu.link = "log"), data=DAT1.F)


The graphs: Model m4

Model m17

Model m24

• These distributions are so extremely close to exhibiting Normality that one is compelled to ask the question, why do these tiny departures from Normality matter in your application?
– whuber
Jan 12 at 15:20
• @ whuber, Thank you very much for your response. We are more interested in residuals ranging between -3 and 3 and any improvement is primarily beyond +3 and -3 z-scores, is unimportant in clinical practice. Although it appears that these three models are the same, do you recommend that I choose one that is at least normal in the -3 to 3 range? or still normality assumption does not matter? Jan 13 at 9:24
• @ whuber, I made the question more clear here, stats.stackexchange.com/questions/601860/… so I would be so thankful if you share your thoughts on it. Jan 13 at 10:41