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Page 1: T0a fhR'S fhe*b'S

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Figure 6: Likelihood Function of τ

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Figure 7: Likelihood Function of φ= log(τ)

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0.0 0.2 0.4 0.6 0.8 1.0

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Figure 8: Likelihood Function of π

π

πt (1−π)24

−t

t=2 t=12 t=22

R�g"�/)&�;���<b�,1IK+�<�)M+�<�)�IK&/&.*x)���(�&,�*Y8-,�8i,17 8(�� <�8-,1+�*�Wi@�7�@ ,j@�%P@��_I�+�,1IK7 +�+�*�)��h+�7�+�(",f<)�M-+�<�)I�&.&/*��PI�8X�+,1IK7 +�+�*�)��h+�7�+�(",�� IY8d�+���@��_I�+�<)�M-+�<�)I�&.&/*��a�6&�7I¦21 �i)���dh&� ), )�+�<b�� M+0W'+�*�]��6&�7V¦31Ñ�>�i)����b.���?+�, 7 )�SW�I�)<�+��6&�7[¦21 ����)��_(K+�:"8-, )�+�<bT� M+0W'+�*�@P (V, I�+'*�+�7 )U�8�,1)�&(V&� (+ �\7�+�b.�$2-d�7 )&�7�),�Wf8�|� +�+�(�,1IY8�,|,1IK+'dY87 8�?+�,1+�7�Wi@�7�@ ,j@aW�I�)�S�IV, I�+'<)�M-+�<�)I�&.&/*)���8d�dK7 &��/)���8-,1+�<b�*Y8-,18�,17 8(���<=8-, +�*O)�V:�)U��+�( g"bF241 � v " �-, o��� AW�/@��_I$;���)�( ,1I�)�VS�8� +TS�&�(���)�*�+�7,1IK+�,17 8(����6&�7 �?+�* d�8718�?+�, +�7�251 � % � " �-, o>�/� %�� � " �-, A %&!���)�( � " %P@76�7 )U,1)(�:e, I�+H<)�M-+�<�)I�&.&/*�6;�(�S0,1)&�( )�(�,1+�7�����&�O2 W�+T:�+0,x2co 2�� 8���1 ��)�( ,-9 2�S�&�� , ³ .;: 9 ¸ 2��6&�7!2 : �=<?> %^Ò����A@ ��&XW ,1I�+H, I�7 +�+��,18(�*Y8-7 *�)NM�+�*e<�)M+�<�)�IK&/&.*��')(�,1+�7����_&-�B29)��_dK<�&,�,1+�*��6&�7[¦@1 �/]BA>��8(�* ����)�(C/|)�:;�7 +ZÓxg�+�<�&XWi@

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Figure 9: Likelihood Function of φ

φ

(sin(φ)

)2t (cos(φ

))48−2

t

t=2 t=12 t=22

d ¿

Page 46: T0a fhR'S fhe*b'S

�_I�+�<�)�M-+�<)�I�&.&/*K��)�(�/|)�:;�7 +IÓ�8-d�dh+�87D,1&�gh+�*Y8-,18c,17 8(���<=8-, +�*�8(�*�, I$;���8c;�(�)�6&7 �ud�7�)�&�7D�6&�7R��)�( : " %*�+�+��{,1&ig�+�f.;K),1+c8dKd�7 &�dK7 )=8�,1+@ �_I�)��P;K(�)�6&�7�� d�7�)�&�7P&(?��)�( : " %e)��?d�<�)+��a, IY8-,�,1IK+-(+ �\7�+�b.�$2$d�7�)�&�7%'&�o %���! % : " �-, o A � %�� : " �-, &(�%P@ Å���������� ��WV®Ç����������'�B�� �dÉ�! P�� &JI Xa&�)� � &(RoZ���0]�<�&�: � o�� � �h��1H�dÂ���<�&�:6�ZÁ �D@ � +�(�S�+ w yw ] y <&�: � o'& � ���1 ww ] o'&�Ò�� � AX��1 � &�Ò�� , @-�_I�+�7 +0�6&�7 +���)�(�S�+�z�] � & � 1 �R] v o��h� 1 zH] � � w�yw ] y <�&�: � o�&�� �h� � 1 � : "�@�_I$;���g"bOoZ� < �0] (+ �\7�+�b.�$2hd�7 )&�7f�6&�7 �9)���:�)�+�(�g$b %'&Yo��h��! � : " �-, ] �S¯ < @q��&, +�, IY8-,�8:"8)( %'&KoZ���)��c)��?d�7�&�dh+�7�@ �_I�+�<�)�M-+�<)�I�&.&/*\]�8��8x�6;�(�S�, )�&�(�&�6�9)���d�<�&,�,1+�*�)�( /|)�:;�7 + A < g�+�<&XWu�6&�7�à 1 A�8-(�*�01 A�] d 8(�*5ÓK@

0 5 10 15 20

0.0

0.1

0.2

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Figure 10: Likelihood Function of λ

λ

λy e−λ

y=1

y=4

y=9

��4x��9�:��%27���%,���� ����'()*�7�('�� +�+�,M'(4|1 +*�x,P5>�"5Y��#"5*1 4$�z5>���%,eARI{#7Is�%I��UI� /;��1 +jA A&� �%1k�"� �.�('()>�%��'(� +�+�,\5>45T-0/ 1 2��"'�+31 +*-N` �� � ����� a��Dd��� ������ ����� ������� �U?]A&#�'^�����%1_5*4��|a�`�� �KdX� ` ����� �����X'(4�: �(+*�$�"�7,-0+3#���� �R4"5*yY���CF>5*��/ �%4!+>-KGM5>4|'�1��K' [ /;#��S�3�Rw��%��+mA��

0 1 2 3 4

0.0

0.2

0.4

0.6

0.8

1.0

Figure 11: Likelihood Function of φ

φ

φ2ye−φ

2

y=1 y=4 y=9

'��E4�/ , ,;�%1 �^V 5*: :��Q5>#�4E�"+�w�� ,P5>�"5��"#�5*1 4��(5>�"�7,@I �!��/;4k5�/ 1;'�-0+3#$y :;#�'(+*#E+31 � � 5*: :��Q5*#$4E�"+�w��#��%5*4�+*1P5*w ���*?P�(�%5*, '�1 [ �"+ �"�;� �*��Z]#$�7V�4"!�: #$'(+3#$#&%Pa'��d!�(� � ����� +31)� I *�!�8/ 4X'�1�5*1k�%4�4$�%1 27�+�*�7ZD#���V�4�!@: #$'(+3#&2Q5��"2B� �74X� +3��,r+*-65Y:P5*#�5*yg���"#$'(2O-0/ 1 2��"'(+*1 `Kac3d!ARI{#7Is�%I&A&�;'(2B�

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