[R] dnorm() lead to a probability >1

[Achim Zeileis]

On Friday 31 October 2003 20:40, Marc Belisle wrote:

> Howdee,
>
> One of my student spotted something I can't explain: a probability
> >1 vs a normal probability density function.
>
> > dnorm(x=1, mean=1, sd=0.4)
>
> [1] 0.9973557
>
> > dnorm(x=1, mean=1, sd=0.39)
>
> [1] 1.022929
>
> > dnorm(x=1, mean=1, sd=0.3)
>
> [1] 1.329808
>
> > dnorm(x=1, mean=1, sd=0.1)
>
> [1] 3.989423
>
> > dnorm(x=1, mean=1, sd=0.01)
>
> [1] 39.89423
>
> > dnorm(x=1, mean=1, sd=0.001)
>
> [1] 398.9423
>
> Is there a bug with the algorithm?

The *area* under the density curve corresponds to the probability in 
the corresponding interval...as you might have learned in a statistics 
course.
So it's perfeclty alright for a density function to exceed 1 if the 
area under the whole curve still equals one. Immediately obvious for
  curve(dunif(x, min = 0, max = 0.5))

hth,
Z

> Thanks,
>
> Marc
>
> ========================
> Marc Bélisle
> Professeur adjoint
> Département de biologie
> Université de Sherbrooke
> 2500 boul. de l'Université
> Sherbrooke, Québec
> J1K 2R1 CANADA
>
> Tél: +1-819-821-8000 poste 1313
> Fax: +1-819-821-8049
> Courriél: Marc.M.Belisle at USherbrooke.ca
> Site Web:
> www.usherbrooke.ca/biologie/recherche/ecologie/Belisle/belisle.html
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help