data = {{$t_{\mathrm{1}}\mathrm{,}{y}_{\mathrm{1}}$},{${\displaystyle t_2,y_2}$},{$t_{\mathrm{3}}\mathrm{,}{y}_{\mathrm{3}}$}...,{$t_{\mathrm{m}}\mathrm{,}{y}_{\mathrm{m}}$}}; $N$= $N_{\mathrm{0}}$; rate = Function[{$a_{\mathrm{1}}$,$a_{\mathrm{2}}$,${\displaystyle k_1}$,$k_{\mathrm{2}}$,t}, Piecewise[{{$a_{\mathrm{1}}$ PDF[HypoexponentialDistribution[Table[i${\displaystyle k_1}$,{i,1,${\displaystyle N}$}]],t] +$a_{\mathrm{2}}$ PDF[HypoexponentialDistribution[Join[Table[i${\displaystyle k_1}$,{i,1,${\displaystyle N}$}],{$k_{\mathrm{2}}$}]],t]                                                      ,t ≥ 0}},0]]; fit = NonlinearModelFit[data,rate[${\displaystyle a_1}$,$a_{\mathrm{2}}$,${\displaystyle k_1}$,$k_{\mathrm{2}}$,t],          {{$a_{\mathrm{1}}$,${\displaystyle a_{10}}$},{$a_{\mathrm{2}}$,$a_{\mathrm{20}}$},{$k_{\mathrm{1}}$,$k_{\mathrm{10}}$},{$k_{\mathrm{2}}$,$k_{\mathrm{20}}$}},t,Method -> "NMinimize"]; fit["ParameterTable"] Mean[Map[Abs, fit["FitResiduals"]]]