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12{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 815 "restart:\nwith(Stat
13istics):\npoisson_:=RandomVariable(Poisson(lambda)):\npdf:=subs(u=n,Pr
14obabilityFunction(poisson_,u));\ncdf:=simplify(subs(u=n,CDF(poisson_,u
15)));\nmu_:=Mean(poisson_);\nvar_:=Variance(poisson_);\nskew_:=simplify
16(convert(Skewness(poisson_),GAMMA),symbolic);\nkurt_:=simplify(convert
17(Kurtosis(poisson_),GAMMA),symbolic);\nqdf:=simplify(Quantile(poisson_
18,q));\nqdf2:=solve(cdf=q,K);\npdfgr:=[factor(diff(pdf, lambda))];\ncdf
19gr:=[diff(cdf, lambda)];\nvalnum:=lambda=10:\nevalf(subs(valnum,n=12,p
20df));\nevalf(subs(valnum,n=12,cdf));\nevalf(subs(valnum,n=12,pdfgr));
21\nevalf(subs(valnum,n=12,cdfgr));\nq:=evalf(Quantile(Poisson(subs(valn
22um,lambda)),0.95));\nevalf(subs(valnum,n=q,cdf));\nevalf(subs(valnum,m
23u_));\nevalf(subs(valnum,sqrt(var_)));\nevalf(subs(valnum,skew_));\nev
24alf(subs(valnum,kurt_));\nevalf(subs(valnum,var_));" }}{PARA 11 "" 1 "
25" {XPPMATH 20 "6#>%$pdfG-%*PIECEWISEG6$7$\"\"!2%\"nGF)7$*()%'lambdaGF+
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27"" 1 "" {XPPMATH 20 "6#>%$cdfG*&-%&GAMMAG6$,&-%&floorG6#%\"nG\"\"\"F.F
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3011 "" 1 "" {XPPMATH 20 "6#>%&skew_G*&\"\"\"F&*$%'lambdaG#F&\"\"#!\"\"
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35{XPPMATH 20 "6#>%%qdf2G6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&pdfgr
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381 "" {XPPMATH 20 "6#>%&cdfgrG7#,$*()%'lambdaG-%&floorG6#%\"nG\"\"\"-%$
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9210 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}
93}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 161 "cdf:=convert(CDF(Gamma(1,
94lambda),n),GAMMA);\ncdf2:=1-GAMMA(lambda,n)/GAMMA(lambda);\ncdf3:=GAMM
95A(n,lambda)/GAMMA(n);\nevalf(subs(lambda=100,n=100,[cdf,cdf2,cdf3]));
96" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$cdfG-%*PIECEWISEG6$7$\"\"!2%\"n
97GF)7$*,-%$expG6#,$*&\"\"#!\"\"F+\"\"\"F4F5,(*&-F/6#,$*&F3F4F+F5F5F5,(-
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100F3F5F+F5F5*(FGF5FJF5FAF5F5F5-F>6#FAF4FAF4FDF41F)F+" }}{PARA 11 "" 1 "
101" {XPPMATH 20 "6#>%%cdf2G,&\"\"\"F&*&-%&GAMMAG6$%'lambdaG%\"nGF&-F)6#F
102+!\"\"F/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%cdf3G*&-%&GAMMAG6$%\"nG
103%'lambdaG\"\"\"-F'6#F)!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%$\"+&
104)z)H8&!#5$\"+#)z)H8&F&$\"+=?,n[F&" }}}{EXCHG {PARA 0 "> " 0 ""
105{MPLTEXT 1 0 51 "with(plots):\nseries(diff(GAMMA(n,x)/GAMMA(n),x),n);
106" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#+/%\"nG,$*&%\"xG!\"\"-%$expG6#,$F'
107F(\"\"\"F(F-,&*(F'F(-%#lnG6#F'F-F)F-F(*(F'F(F)F-%&gammaGF-F(\"\"#,(*&#
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140" {MPLTEXT 1 0 126 "for i from 0 to 99 do\n  level:=(0.5+i)/100.0;\n  \+
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143\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+++++:!#6$\"\"%\"\"!" }}
144{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+++++D!#6$\"\"%\"\"!" }}{PARA 11
145"" 1 "" {XPPMATH 20 "6#7$$\"+++++N!#6$\"\"&\"\"!" }}{PARA 11 "" 1 ""
146{XPPMATH 20 "6#7$$\"+++++X!#6$\"\"&\"\"!" }}{PARA 11 "" 1 "" {XPPMATH
14720 "6#7$$\"+++++b!#6$\"\"&\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$
148\"+++++l!#6$\"\"&\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+++++v!
149#6$\"\"'\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+++++&)!#6$\"\"'
150\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+++++&*!#6$\"\"'\"\"!" }
151}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"++++]5!#5$\"\"'\"\"!" }}{PARA
15211 "" 1 "" {XPPMATH 20 "6#7$$\"++++]6!#5$\"\"'\"\"!" }}{PARA 11 "" 1 "
153" {XPPMATH 20 "6#7$$\"++++]7!#5$\"\"'\"\"!" }}{PARA 11 "" 1 ""
154{XPPMATH 20 "6#7$$\"++++]8!#5$\"\"(\"\"!" }}{PARA 11 "" 1 "" {XPPMATH
15520 "6#7$$\"++++]9!#5$\"\"(\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$
156\"++++]:!#5$\"\"(\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"++++];!
157#5$\"\"(\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"++++]<!#5$\"\"(
158\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"++++]=!#5$\"\"(\"\"!" }}
159{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"++++]>!#5$\"\"(\"\"!" }}{PARA 11
160"" 1 "" {XPPMATH 20 "6#7$$\"++++]?!#5$\"\"(\"\"!" }}{PARA 11 "" 1 ""
161{XPPMATH 20 "6#7$$\"++++]@!#5$\"\"(\"\"!" }}{PARA 11 "" 1 "" {XPPMATH
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165\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"++++]E!#5$\"\")\"\"!" }}
166{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"++++]F!#5$\"\")\"\"!" }}{PARA 11
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168{XPPMATH 20 "6#7$$\"++++]H!#5$\"\")\"\"!" }}{PARA 11 "" 1 "" {XPPMATH
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173{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"++++]N!#5$\"\"*\"\"!" }}{PARA 11
174"" 1 "" {XPPMATH 20 "6#7$$\"++++]O!#5$\"\"*\"\"!" }}{PARA 11 "" 1 ""
175{XPPMATH 20 "6#7$$\"++++]P!#5$\"\"*\"\"!" }}{PARA 11 "" 1 "" {XPPMATH
17620 "6#7$$\"++++]Q!#5$\"\"*\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$
177\"++++]R!#5$\"\"*\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"++++]S!
178#5$\"\"*\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"++++]T!#5$\"\"*
179\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"++++]U!#5$\"\"*\"\"!" }}
180{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"++++]V!#5$\"\"*\"\"!" }}{PARA 11
181"" 1 "" {XPPMATH 20 "6#7$$\"++++]W!#5$\"\"*\"\"!" }}{PARA 11 "" 1 ""
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