title: Can correlation between fit parameters cause this function to not fit data?
body: <pre><code>from lmfit import Model
  
  def PSF_fit(r,beta,alpha):
  R=((beta-1)/(3.14*alpha*alpha))*((1+ (r / alpha)**2)**(-beta))
  return R
  
  moffat = Model(PSF_fit)
  
  print(f'parameter names: {moffat.param_names}')
  print(f'independent variables: {moffat.independent_vars}')
  
  params = moffat.make_params(beta=2.85,alpha=1.5)
  
  result = moffat.fit(Intensity, params,r=r)
  
  print(result.fit_report())
  
  plt.rcParams.update({'font.size': 14})
  plt.figure(figsize = (10,7))
  plt.plot(r,Intensity, 'bo')
  
  plt.plot(r, result.init_fit, '--', label='initial fit')
  plt.plot(r, result.best_fit, '-', label='best fit')
  plt.xlabel('Radius(pixels)')
  plt.ylabel('Saturation corrected profile')
  plt.legend()
  plt.title('Circular Moffat Fit')
  plt.show()
  </code></pre>
  <p>I was trying to fit the above mentioned circular moffat function to a Flux profile. But it doesn't seem to fit. My fit report is as follows:</p>
  <pre><code>parameter names: ['beta', 'alpha']
  independent variables: ['r']
  [[Model]]
  Model(PSF_fit)
  [[Fit Statistics]]
  # fitting method   = leastsq
  # function evals   = 248
  # data points      = 28
  # variables        = 2
  chi-square         = 127948.959
  reduced chi-square = 4921.11382
  Akaike info crit   = 239.961102
  Bayesian info crit = 242.625511
  [[Variables]]
  beta:   18.2260915 +/- 1845366.32 (10124860.41%) (init = 2.85)
  alpha:  9.61025099 +/- 553166.734 (5756007.15%) (init = 1.429321)
  [[Correlations]] (unreported correlations are &lt; 0.100)
  C(beta, alpha) = 0.999
  </code></pre>
  <p>Can the correlation between alpha and beta be causing this?</p>
  <p>This is the fit result. <a href="https://i.stack.imgur.com/PFGSL.png" rel="nofollow noreferrer">Fit result for circular Moffat</a></p>