Lottery Game
by
Pedro Marquez
Load Libraries, Data and Initialize Game
## CONCURSO R1 R2 R3 R4 R5 R6
## 1 2909 3 4 7 30 45 52
## 2 2908 5 13 23 33 44 56
## 3 2907 1 15 17 25 37 45
## 4 2906 5 15 28 37 46 49
## 5 2905 4 27 41 45 48 54
## 6 2904 3 15 20 36 40 56
## 7 2903 7 20 23 24 27 42
## 8 2902 5 16 25 27 35 45
## 9 2901 2 8 9 25 46 52
## 10 2900 2 13 18 20 21 52
## 11 2899 13 18 30 33 36 51
## 12 2898 10 18 25 33 38 49
## 13 2897 4 8 24 25 26 37
## 14 2896 9 10 15 41 46 49
## 15 2895 16 19 30 38 40 49
## 16 2894 12 13 16 26 30 49
## 17 2893 2 22 28 32 33 51
## 18 2892 1 3 5 24 42 46
## 19 2891 15 22 27 28 30 31
## 20 2890 8 16 17 26 31 37
## 21 2889 3 16 20 28 40 55
## 22 2888 13 14 23 35 37 40
## 23 2887 23 25 29 33 46 49
## 24 2886 5 13 19 29 30 56
## 25 2885 1 11 20 27 39 41
## 26 2884 2 16 30 35 51 53
## 27 2883 11 12 17 32 36 54
## 28 2882 1 15 26 30 49 52
## 29 2881 19 22 41 48 51 55
## 30 2880 12 16 30 32 37 49
## 31 2879 6 9 27 32 37 44
## 32 2878 1 5 10 17 34 40
## 33 2877 1 17 20 29 35 51
## 34 2876 3 16 28 30 40 54
## 35 2875 2 4 16 38 50 52
## 36 2874 3 6 23 25 34 35
## 37 2873 1 4 11 17 44 52
## 38 2872 4 10 12 22 32 51
## 39 2871 16 24 32 36 51 52
## 40 2870 14 33 42 45 51 55
## 41 2869 2 20 31 35 48 53
## 42 2868 1 10 11 33 37 47
## 43 2867 3 26 27 38 44 56
## 44 2866 7 8 23 34 47 52
## 45 2865 3 4 17 19 21 49
## 46 2864 7 23 25 29 33 50
## 47 2863 21 25 27 36 47 54
## 48 2862 11 12 18 40 53 56
## 49 2861 5 7 29 36 38 41
## 50 2860 9 14 22 35 37 47
## 51 2859 24 29 42 44 52 53
## 52 2858 10 28 33 37 46 52
## 53 2857 2 11 16 24 31 37
## 54 2856 6 15 20 24 37 51
## 55 2855 4 8 10 18 46 56
## 56 2854 7 18 23 31 35 36
## 57 2853 4 10 40 42 45 46
## 58 2852 5 6 14 15 31 46
## 59 2851 24 25 26 32 39 47
## 60 2850 3 7 17 38 39 50
## 61 2849 3 31 39 43 44 50
## 62 2848 22 33 40 41 42 48
## 63 2847 8 34 43 49 54 55
## 64 2846 9 18 28 29 41 50
## 65 2845 8 11 22 23 38 41
## 66 2844 11 17 19 24 43 49
## 67 2843 17 22 24 31 43 50
## 68 2842 4 5 25 35 48 53
## 69 2841 6 8 29 47 48 50
## 70 2840 4 25 31 44 49 56
## 71 2839 3 10 19 34 44 54
## 72 2838 8 9 11 20 22 40
## 73 2837 3 6 25 45 46 48
## 74 2836 3 6 11 24 31 51
## 75 2835 1 2 13 27 29 34
## 76 2834 6 17 27 32 34 40
## 77 2833 1 10 12 32 36 48
## 78 2832 24 27 40 41 54 55
## 79 2831 3 6 14 28 30 39
## 80 2830 5 12 22 41 44 47
## 81 2829 1 15 26 40 45 46
## 82 2828 4 15 18 30 38 49
## 83 2827 1 5 17 25 35 55
## 84 2826 9 14 35 46 49 55
## 85 2825 8 17 20 38 54 56
## 86 2824 8 17 19 36 37 41
## 87 2823 11 21 33 43 54 55
## 88 2822 12 22 36 43 46 52
## 89 2821 9 13 29 33 39 51
## 90 2820 6 16 21 32 43 56
## 91 2819 2 5 18 30 44 53
## 92 2818 12 31 37 44 52 55
## 93 2817 7 21 33 35 43 55
## 94 2816 3 6 22 38 40 56
## 95 2815 17 19 22 23 36 38
## 96 2814 9 17 22 26 49 56
## 97 2813 2 8 16 23 42 48
## 98 2812 28 30 32 34 42 43
## 99 2811 2 29 30 36 44 51
## 100 2810 6 30 34 46 50 52
## 101 2809 20 32 33 34 50 56
## 102 2808 10 17 20 31 50 51
## 103 2807 8 9 14 28 33 56
## 104 2806 11 12 17 29 30 34
## 105 2805 1 13 21 22 33 45
## 106 2804 3 10 14 28 48 56
## 107 2803 8 12 19 21 22 43
## 108 2802 11 22 25 29 37 55
## 109 2801 19 26 37 50 53 54
## 110 2800 8 15 35 37 41 48
## 111 2799 13 14 16 28 50 51
## 112 2798 8 14 20 42 43 55
## 113 2797 4 5 16 29 39 55
## 114 2796 2 17 39 48 53 56
## 115 2795 8 20 26 27 42 44
## 116 2794 7 8 20 37 39 45
## 117 2793 6 12 40 43 51 56
## 118 2792 8 13 18 22 40 54
## 119 2791 4 8 11 37 41 43
## 120 2790 33 35 47 52 53 56
## 121 2789 7 17 40 48 53 56
## 122 2788 3 6 40 41 47 48
## 123 2787 3 5 19 24 28 30
## 124 2786 4 15 16 30 44 50
## 125 2785 2 13 21 35 41 49
## 126 2784 3 29 30 38 42 50
## 127 2783 18 24 31 39 47 51
## 128 2782 1 3 16 19 20 28
## 129 2781 10 14 16 17 27 49
## 130 2780 1 5 6 8 30 46
## 131 2779 13 21 37 42 43 48
## 132 2778 1 3 12 22 35 55
## 133 2777 11 18 21 31 36 49
## 134 2776 5 8 26 32 37 39
## 135 2775 2 6 30 34 37 43
## 136 2774 12 25 31 36 46 54
## 137 2773 9 18 40 42 48 52
## 138 2772 5 26 30 34 37 56
## 139 2771 5 13 15 40 54 55
## 140 2770 14 18 50 51 52 56
## 141 2769 6 11 27 33 41 56
## 142 2768 5 7 44 51 53 54
## 143 2767 2 4 26 27 28 44
## 144 2766 4 15 16 34 44 56
## 145 2765 2 14 21 28 36 49
## 146 2764 10 23 29 45 53 56
## 147 2763 1 6 15 22 34 39
## 148 2762 14 33 41 43 52 56
## 149 2761 4 8 15 36 39 45
## 150 2760 4 11 12 40 45 51
## 151 2759 12 15 31 50 54 55
## 152 2758 12 20 33 46 50 51
## 153 2757 6 18 36 48 50 52
## 154 2756 5 6 33 34 46 55
## 155 2755 4 20 29 31 44 48
## 156 2754 11 18 31 35 39 42
## 157 2753 8 16 21 39 50 52
## 158 2752 15 17 19 22 31 53
## 159 2751 10 22 29 30 32 33
## 160 2750 6 19 23 25 28 42
## 161 2749 8 11 14 36 49 55
## 162 2748 2 14 27 42 46 50
## 163 2747 34 44 45 51 52 56
## 164 2746 7 11 26 38 39 56
## 165 2745 1 13 19 29 41 46
## 166 2744 1 9 12 19 31 34
## 167 2743 1 2 4 31 32 46
## 168 2742 10 26 40 44 50 54
## 169 2741 1 4 20 21 24 34
## 170 2740 28 31 32 44 51 52
## 171 2739 5 16 17 24 41 47
## 172 2738 4 6 20 21 45 55
## 173 2737 16 19 23 29 33 49
## 174 2736 7 24 27 39 45 52
## 175 2735 13 18 26 30 31 53
## 176 2734 2 7 10 27 34 54
## 177 2733 10 15 23 24 36 49
## 178 2732 3 6 19 28 48 52
## 179 2731 2 3 7 26 30 48
## 180 2730 5 7 8 23 26 55
## 181 2729 7 9 29 44 48 55
## 182 2728 5 16 30 31 38 52
## 183 2727 2 9 15 16 21 42
## 184 2726 7 14 23 26 43 49
## 185 2725 6 13 27 32 47 52
## 186 2724 13 15 19 33 49 53
## 187 2723 7 10 13 23 34 44
## 188 2722 1 5 28 48 49 55
## 189 2721 5 6 7 25 33 50
## 190 2720 24 30 40 41 55 56
## 191 2719 9 10 30 35 41 48
## 192 2718 5 13 20 32 36 56
## 193 2717 7 26 31 44 45 53
## 194 2716 8 16 18 46 52 55
## 195 2715 6 13 17 20 31 50
## 196 2714 4 5 22 28 31 37
## 197 2713 5 15 24 25 37 39
## 198 2712 2 7 12 35 51 54
## 199 2711 7 13 23 37 48 49
## 200 2710 10 29 32 42 43 47
## 201 2709 2 10 25 30 32 56
## 202 2708 4 5 30 43 45 51
## 203 2707 8 9 12 30 43 51
## 204 2706 4 9 20 25 28 37
## 205 2705 4 13 22 34 37 39
## 206 2704 4 19 24 39 49 55
## 207 2703 3 4 18 20 26 28
## 208 2702 8 9 23 37 48 53
Visualyzing Distributions
Selecting Distribution Type (for R1: Beta or Gamma)
## summary statistics
## ------
## min: 1 max: 34
## median: 6
## mean: 7.360577
## estimated sd: 6.196445
## estimated skewness: 1.719955
## estimated kurtosis: 6.508291
Analysing All Random Variables
See if they look Gaussian: \(\displaystyle f(x;\mu,\lambda) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}\)
## mean sd skewness kurtosis
## 1: 7.360577 6.196445 1.70752637 right 6.395815 sharper
## 2: 14.860577 8.019589 0.70374365 right 3.148156 sharper
## 3: 23.980769 9.221882 0.33267933 right 2.682649 flatter
## 4: 32.990385 8.584893 0.05643897 right 2.498910 flatter
## 5: 40.855769 8.245530 -0.35455961 left 2.389366 flatter
## 6: 49.187500 6.447741 -1.15466654 left 3.786478 sharper
Fitting a Distribution (R1)
## Fitting of the distribution ' beta ' by maximum likelihood
## Parameters:
## estimate Std. Error
## shape1 0.911517 0.0786541
## shape2 2.704400 0.2752100
## [1] -169.8144
Density Curve vs. Simulated Distribution
Checking Normality (of R1)
Suggested Game
(Showing Only Suggested Numbers for R1)
## Game 1 Game 2 Game 3
## 1: 25 8 27
## 2: 0 0 0
## 3: 0 0 0
## 4: 0 0 0
## 5: 0 0 0
## 6: 0 0 0
