U md(@sdZddlZddlmZddlmZddlmZddl m Z ddlm Z m Z ddlmZGdd d eZed d d d dZd\ZZZedZdddddgZdefdefdefdefdeffD]<\ZZeeeeeeeeeeejeee eeqeejeeeddeejje eeddeeeeeeeje eeddZdd Zd!d"Z d#d$Z!d;d(d)Z"ee!dd*d&ee!dd+d&ej#d,dd-d.Z$e"e$d/d0d1Z%ee%d0d2dee%dd2dd3d4Z&d5d6Z'e&d7ed0d&\Z(Z)Z*ee(ee)ee*ee'ej+dd8ee'ej+ej d*ddgd8ej+j#d9d:Z#e#e#,Z#ee#,e#e#d*k,e#e#dk,e#e#dk,dS)u ~ GPD(k, sigma-k*u) if x ~ GPD(k, sigma) notation of de Zea Bermudez, Kotz k, sigma is shape, scale rthreshshapescalerrr paramstopotRsr5cCs||||fS)Nr)r2r3Zscalepotrrr paramsfrompot\sr6cCs|st|ddS)Nz does not hold)print)Zcondmsgrrrwarnif`sr9cCsFt|dkdt|dkdt|||dkd|||d|S)zemean excess function of genpareto assert are inequality conditions in de Zea Bermudez, Kotz r z shape > -1rz thresh >= 0z(scale - shape*thresh) > 0r )r9r1rrr meanexcessesr:d empc Cs|dkr|dkrtqn|dkrt|}|dddtdt|d|ddd}|ddd}|rt|d| |d| |dk r|\}} t|d| | |d| |d|||fS)NZestr=r r r )NotImplementedErrorr sortcumsumr!lenpltplot) dataparamsZlidxZuidxmethodrC datasortedr:r3r4rrrmeanexcess_plotps 4 0rHgi)r4size)rJr0r )rErCicCst|t}|dddtdt|d|ddd}|dddtdt|d}|ddd}|||dddfS)Nr r )r r?Zastypefloatr@r!rA)rDrGr:Zmeancontrrrmeanexcess_emps 4&rMcs8t|dkrj|ddStfdd|DSdS)NrTlbZ conditionalcsg|]}j|ddqS)TrN)expect).0Zlbbrrr sz#meanexcess_dist..)r ndimrParray)rrOargskwdsrrRrmeanexcess_dists rXr )rOi)rK)Nr;r<r=r)-__doc__numpyr ZscipyrZ scipy.specialrZscipy.stats.distributionsrZmatplotlib.pyplotZpyplotrBrrrr rZ genpareto2r3locr4r!rvZquantrFrr7getattrr+Zentropyr5r6r9r:rHZrvsrDtmprMrXZdsmeZmcZnormZmeanrrrrsd     !       6