title: Multiple Minimums in R
body: <p>I am trying to find the values which contribute the most and least to a Guassian Kernel Density estimator. I've written a function to find these, but I'm getting multiple values for a max when I run it. I thought this might be related to the number of significant digits, so I increased those but nothing changed. </p>
  
  <p>Can anyone offer some insight?</p>
  
  <pre><code>#Create a vector with Brainsize-Small Litter Size Data:
  Y_i&lt;-c(0.42, 0.86, 0.88, 1.11, 1.34, 1.38, 1.42, 1.47, 1.63,1.73, 2.17, 2.42, 2.48, 2.74, 2.74, 2.79, 2.90, 3.12,3.18, 3.27, 3.30, 3.61, 3.63, 4.13, 4.40, 5.00, 5.20,5.59, 7.04, 7.15, 7.25, 7.75, 8.00, 8.84, 9.30, 9.68,10.32, 10.41, 10.48, 11.29, 12.30, 12.53, 12.69, 14.14, 14.15,14.27, 14.56, 15.84, 18.55, 19.73, 20.00)
  
  #Create a kernel density estimator function:
  kern&lt;-function(data=0,effOf=0,bw=0){
  z&lt;-rep(0,length(data))
  k&lt;-rep(0,length(data))
  
  for(i in data){
   z[i]=((effOf-data[i])/bw)
  }
  
  for(j in z){
   k[j]=(1/sqrt(2*pi))*exp(-(z[j]^2/2))/(length(data)*bw)
  }
  
  min=min(k)
  imin=which(k==min)
  ymin=data[imin]
  
  max=max(k)
  imax=which(k==max)
  ymax=data[imax]
  
  print(paste("The minimum contributor is value",ymin))
  print(paste("The maximum contributor is value",ymax))
  
  estimate=sum(k)
  return(estimate)
  }
  
  #(a.)Use KDE function to estimate f(16)
  kern(Y_i,16,3)
  </code></pre>
  
  <p>This is the output- keep in mind that I only want one maximum value:</p>
  
  <pre><code> [1] "The minimum contributor is value 0.42"  "The minimum contributor is value 0.86" 
   [3] "The minimum contributor is value 0.88"  "The minimum contributor is value 1.38" 
   [5] "The minimum contributor is value 1.42"  "The minimum contributor is value 1.47" 
   [7] "The minimum contributor is value 1.63"  "The minimum contributor is value 1.73" 
   [9] "The minimum contributor is value 2.17"  "The minimum contributor is value 2.42" 
  [11] "The minimum contributor is value 2.48"  "The minimum contributor is value 2.74" 
  [13] "The minimum contributor is value 2.74"  "The minimum contributor is value 2.79" 
  [15] "The minimum contributor is value 2.9"   "The minimum contributor is value 3.12" 
  [17] "The minimum contributor is value 3.18"  "The minimum contributor is value 3.27" 
  [19] "The minimum contributor is value 3.3"   "The minimum contributor is value 3.61" 
  [21] "The minimum contributor is value 3.63"  "The minimum contributor is value 4.13" 
  [23] "The minimum contributor is value 4.4"   "The minimum contributor is value 5"    
  [25] "The minimum contributor is value 5.2"   "The minimum contributor is value 5.59" 
  [27] "The minimum contributor is value 7.04"  "The minimum contributor is value 7.15" 
  [29] "The minimum contributor is value 7.25"  "The minimum contributor is value 7.75" 
  [31] "The minimum contributor is value 8"     "The minimum contributor is value 8.84" 
  [33] "The minimum contributor is value 9.3"   "The minimum contributor is value 9.68" 
  [35] "The minimum contributor is value 10.32" "The minimum contributor is value 10.41"
  [37] "The minimum contributor is value 10.48" "The minimum contributor is value 11.29"
  [39] "The minimum contributor is value 12.3"  "The minimum contributor is value 12.53"
  [41] "The minimum contributor is value 12.69" "The minimum contributor is value 14.14"
  [43] "The minimum contributor is value 14.15" "The minimum contributor is value 14.27"
  [45] "The minimum contributor is value 14.56" "The minimum contributor is value 15.84"
  [47] "The minimum contributor is value 18.55" "The minimum contributor is value 19.73"
  [49] "The minimum contributor is value 20"   
  [1] "The maximum contributor is value 1.34"
  [1] 2.868016e-08
  </code></pre>