The Location-Scale Mixture Exponential Power Distribution: A Bayesian and Maximum Likelihood Approach

<table>(a) Index plot of <svg height="15.65" id="M488" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 28.65 15.65" width="28.65" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,0,0,-.017,.062,11.363)"><path d="M692 302v-28q-45 -6 -54.5 -17t-9.5 -55v-86q0 -62 7 -95q-7 -2 -32 -7.5l-37 -8l-35.5 -7.5t-40.5 -7t-38.5 -4t-40.5 -2q-165 0 -266 93t-101 243q0 84 32 151t86 108t121.5 63t142.5 22q29 0 62.5 -4t52 -7.5t47.5 -10.5t31 -7l15 -156l-28 -6q-17 87 -66.5 121.5
t-128.5 34.5q-117 0 -191 -80.5t-74 -216.5q0 -56 17 -110t49.5 -100.5t87.5 -74.5t124 -28q53 0 87 17q17 9 24.5 23t7.5 43v85q0 54 -15.5 67.5t-89.5 18.5v28h254z" id="x47"></path></g><g transform="matrix(.017,0,0,-.017,12.217,11.363)"><path d="M43 650h280q194 0 282 -85q85 -82 85 -215q0 -173 -123 -267q-107 -83 -297 -83h-236v27q65 5 79.5 19.5t14.5 77.5v402q0 45 -6 62.5t-21.5 24t-57.5 9.5v28zM213 547v-416q0 -55 24.5 -75t81.5 -20q133 0 203 86t70 214q0 80 -30 143t-88 97q-66 41 -170 41
q-62 0 -78 -13q-13 -9 -13 -57z" id="x44"></path></g>
<g transform="matrix(.012,0,0,-.012,24.713,15.45)"><path d="M244 607q0 -25 -15.5 -43t-37.5 -18q-19 0 -32 13t-13 35q0 21 15 41t39 20q20 0 32 -14t12 -34zM222 91q-29 -33 -79 -68t-75 -35q-13 0 -19 7.5t-6 31t10 65.5l62 253q5 26 -1 26q-21 0 -72 -43l-13 24q43 40 91 68t71 28q30 0 10 -78l-71 -274q-8 -30 3 -30
q16 0 76 48z" id="x1D456"></path></g>
</svg> for case weights perturbation for simulated data. (b) Index plot of <svg height="15.4" id="M489" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 25.637501 15.4" width="25.637501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,0,0,-.017,.062,11.113)"><path d="M495 163l30 -6q-19 -99 -36 -157h-453v28q63 5 77.5 20t14.5 78v400q0 63 -13 77t-75 19v28h261v-28q-61 -5 -74.5 -19t-13.5 -77v-395q0 -41 5 -59t18 -25q24 -13 96 -13q85 0 112 31q30 33 51 98z" id="x4C"></path></g><g transform="matrix(.017,0,0,-.017,9.208,11.113)"><path d="M43 650h280q194 0 282 -85q85 -82 85 -215q0 -173 -123 -267q-107 -83 -297 -83h-236v27q65 5 79.5 19.5t14.5 77.5v402q0 45 -6 62.5t-21.5 24t-57.5 9.5v28zM213 547v-416q0 -55 24.5 -75t81.5 -20q133 0 203 86t70 214q0 80 -30 143t-88 97q-66 41 -170 41
q-62 0 -78 -13q-13 -9 -13 -57z" id="x44"></path></g>
<g transform="matrix(.012,0,0,-.012,21.7,15.188)"><path d="M244 607q0 -25 -15.5 -43t-37.5 -18q-19 0 -32 13t-13 35q0 21 15 41t39 20q20 0 32 -14t12 -34zM222 91q-29 -33 -79 -68t-75 -35q-13 0 -19 7.5t-6 31t10 65.5l62 253q5 26 -1 26q-21 0 -72 -43l-13 24q43 40 91 68t71 28q30 0 10 -78l-71 -274q-8 -30 3 -30
q16 0 76 48z" id="x1D456"></path></g>
</svg> for case weights perturbation for simulated data.</table>

Journal of Applied Mathematics

fig5

Figure 5

Figure 5: The Location-Scale Mixture Exponential Power Distribution: A Bayesian and Maximum Likelihood Approach 