       # Extracting parameters from NonlinearFit

```Recently I began writing a program to do a monte carlo simulation of an
NMR experiment. The whole routine is attached (I hope that works.) The
problem is this:
I perform a NonlinearFit utilizing an exponential function of the form
Exp[-a*x]. The nonlinear fit gives me back an equation, something like
1*E(-a*x). I want to extract the a parameter out of the equation and do
two things with it. Because I am performing this simulation several
(thousand) times, I want to know the standard deviation of the a
parameters. Second, I would like to get an average of the terms
(without having to use the last two lines of my code). If anyone out
there could help me out, I would greatly appreciate it; I'm really
stuck.

(PS, if you try to run my code, you may want to change the number of
iterations to 10 or so. 10000 iterations takes a couple of hours.)

Jeff Wank
Dept of Chemistry & Biochemistry
(303) 492-8085

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(*
This routine takes a set of times, t, and fits a curve of the form \
y=init*exp(-bx)
where b is the rate constant (lamda) *)\
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Cell[CellGroupData[{

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\(Needs["\<Statistics`ContinuousDistributions`\>"]\),
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\(Clear[t, init, di, a, ndist, n, values, newlist, aone, lamda1,
loga]\n
\n (*time\ values*) \),
\(t = { .004,  .006,  .008,  .010,  .012,  .016,  .020,  .024,
.028}; \n
\n (*\ initial\ \((0\ time)\)\ value\ *) \ninit = 5.855\ 10\^7; \ \n
\n (*\ error\ in\ normalized\ intensity, \
as\ computed\ from\ 10\ ms\ data\ repetitions\ *) \ndi =  .00757;
\n
\n (*a\ normal\ distribution\ of\ numbers\ *) \n
ndist = NormalDistribution[0, di\ init]; \n
\n (*\ initial\ value\ for\ lamda, \ the\ rate\ constant\ *) \n
lamda = 49.95; \n\n (*\ number\ of\ iterations\ *) \nn = 1; \n\n
a[i_, t_] := init\ Exp[\(-lamda\)\ t] + Random[ndist]; \n
values = \((a[#1, t]&)\)/@Table[i, {i, 1, n}]; \n
newlist = \((Transpose[{t, #1}]&)\)/@values; \n
\n (*fitting\ the\ data*) \n\n\t
lamda1\  = \
\((NonlinearFit[newlist[\([#]\)], init*Exp[\(-a\)*x], {x}, {a,
c}]&)\)/@
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```

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