# [R] Query on finding root

ASHLIN VARKEY @@h||nv@rkey @end|ng |rom gm@||@com
Fri Aug 25 18:47:05 CEST 2023

```Sir,
I want to solve the equation Q(u)=mean, where Q(u) represents the quantile
function. Here my Q(u)=(c*u^lamda1)/((1-u)^lamda2), which is the quantile
function of Davies (Power-pareto) distribution.  Hence I want to solve ,
*(c*u^lamda1)/((1-u)^lamda2)=28353.7....(Eq.1)*
where lamda1=0.03399381, lamda2=0.1074444 and c=26104.50. When I used the
package 'Davies' and solved Eq 1, I got the answer u=0.3952365. But when I
use the function  'uniroot' to solve the Eq.1, I got a different answer
which is  u=0.6048157.  Why did this difference happen?  Which is the
correct method to solve Eq.1. Using the value of *u *from the first method
my further calculation was nearer to empirical values.  The R-code I used
is herewith. Kindly help me to solve this issue.

R-code
Q(u)=(c*u^lamda1)/((1-u)^lamda2)
mean=28353.7 # mean calculated from data
lamda1=.03399381 # estimates c, lamda1 and lamda2 calculated from data
lamda2=.1074444
c=26104.50
library(Davies)# using package
params=c(c,lamda1,lamda2)
u=pdavies(28353.7,params)
u
fun=function(u){((26104.50*u^0.03399381)/((1-u)^0.1074444))-28353.7}
uniroot= uniroot(fun,c(0.01,1))
uniroot

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