How to improve fit of distribution to data I'm trying to fit one of common expenential distributions to data using histfit. However it seems that results aren't as good as expected - it seems that peak should be higher. Histograms presents time interval of occurence of some event versus number of occurences. I tried histfit for Gamma and lognormal distributions.
My question is if is there a way to get better fit for this data? Does number of bins have infulence on result? (maybe better to use fitdistr?) Maybe I can somehow modify fitting funtion to have other cost function and thus get better fit? My goal is to have as good fit as possible.
I'm using Matlab but I can use R as well if necessary.
Data (time intervals) is here.
Results are presented on figure below:

Clarification:
In response to questions about the goal of this study: The data describes process of intervals between vehicles in traffic. I've got several dozens of data files of this kind, all are similar to this one, presented data is good representative. My goal is to fit distribution so I can sample data of this kind.
 A: I cut / pasted individual observations from the link provided. A distribution
ID program yielded essentially the same 'best fit' as @JamesPhillips mentions. 
The binning of the histogram has nothing to do with such distribution ID
procedures, which use individual observations.
In R, density with the default KDE at 1.5 the default bandwidth gave
the red curve below. (The KDE may look like it is smoothing the histogram, but it is determined independently of the histogram.) 
Perhaps @JimB's suggestion is best, unless there
is something clear to be gained from having a name to attach to an
approximating density.

Depending on your objectives, perhaps it is useful to try to understand
the mechanism that produces these data. Is it possible that the distribution
we're observing is a mixture of several simpler distributions? In particular, I suspect that the outliers at the far right (beyond about 300) are interfering with distribution
ID. Do you
think they could be noise unrelated to the
process under study, or do you suppose they are inherent in the process?
x = c(135,346,363,351,154,82,147,...,52,81,14,733,872,730,600)

 hist(x,br=20, prob=T, ylim=c(0,0.008), col="skyblue2")
 rug(x)
 lines(density(x, from=0, to=500, adj=1.5), col="red", lwd=2)

 summary(x); sd(x)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    1.0    89.0   119.0   147.6   163.5   872.0 
 [1] 109.4539

Addendum: Truncating the data to values between 10 and 300 I got
semi-promising probability plots for Weibull and Gamma distributions.
(Plots look vaguely plausible but data fail Anderson-Darling GOF tests.)
Such fussing with data to 'get a fit' is a potentially endless and pointless game,
but I couldn't resist one more try. Please seriously consider @whuber's Comment. (Partial Minitab output.)
  N    Mean   StDev  Minimum     Q1  Median      Q3  Maximum
348  124.01   54.86    10.00  86.00  111.50  150.00   288.00

Distribution    Shape      Scale
Weibull       2.39387  140.03773
Gamma         4.99392   24.83193


