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ӦͦϦ? ?̦̦ ? ̦Ϧͦ?˦ ҦӦ ɦ?ʦǦҦ ɦͦ?ͦئ
- 2. ?̦զئͦ ̦ ЦǦ??, ӦͦϦ? ?̦̦ ŦЦɦͦ?ȦǦʦ ? ӦϦ Karl Pearson. Ԧ?ѦӦǦҦ ?̦̦ , ϦЦ? ?ͦ ЦѦ?ӦǦӦ æɦ ӦϦ ԦЦϦ˦ϦæɦҦ? Ӧ? ʦӦͦϦ??, Ŧ̦զ?ҦӦǦʦ ҦӦ ?Ѧ Ӧ? Ŧئ?? ʦ Ӧئ ɦȦͦϦ?Ӧئ ҦӦ ?Ҧ ӦϦ 18Ϧ ?ͦ, ? ӦϦ ̦ȦǦ̦Ӧɦ? Leonard Euler. ʦϦ?? Ӧ? ҦԦ?ѦӦǦҦ? ?Ӧ,Ѧ֦ɦ??, ̦ɦ æŦ?ʦŦԦҦ Ӧ? ЦѦæϦͦӦɦ?? ҦԦ?ѦӦǦҦ? æɦ ̦-?ѦɦϦ? ѦɦȦ̦??. Ӧ ȦŦئ? ɦȦͦϦ?Ӧئ, ʦӦͦϦ? ?̦̦ ?ͦ ̦ɦ ĦɦЦѦ̦ŦӦѦɦ? ϦɦʦϦ?ͦŦɦ ʦӦͦϦ?. ?Ѧ֦ϦԦ 3 ĦԦͦ?? ЦѦ̦ŦӦѦϦЦϦ?ҦŦ? Ӧ? ʦӦͦϦ??: 1. ?̦ŦӦѦ? Ҧ?̦Ӧ? ʦ Ц?̦ŦӦѦ? ʦ?̦ʦ? 2. ?̦ŦӦѦ? Ҧ?̦Ӧ? ʦ ͦ?ҦӦѦϦզ Ц?̦ŦӦѦ ʦ?̦ʦ? =1/ 3. ?̦ŦӦѦ? Ҧ?̦Ӧ? ʦ Ц?̦ŦӦѦ? ?Ҧ? Ӧɦ?? =/ (Ӧ Ц˦?Ҧɦ Ӧ? ҦԦæʦŦʦѦɦ?ͦ? ŦѦæ?? Ȧ ?ͦŦ ֦?Ҧ Ӧ? 1? ЦѦ̦ŦӦѦϦЦ?ǦҦ?) ? ӦǦ ŦɦĦɦ? ЦŦ?ЦӦئҦ ?ЦϦ Ӧ ?ͦ ԦҦɦ?? ѦɦȦ??, ?Ӧ ʦӦͦϦ? ʦ˦?Ӧ ӦͦϦ? Erlang (ҦԦ?Ȧ?, Ԧ? ЦѦϦ?ЦӦŦ ? ?ȦѦϦɦҦ̦ ʦȦŦӦɦ? ӦͦϦ? ̦ Ц?̦ŦӦѦ ) ? ӦǦ ŦɦĦɦ? ЦŦ?ЦӦئҦ ЦϦ Ӧ ɦҦ?Ӧ ̦ 1, ?Ӧ ӦͦϦ? ?̦̦ ̦ ЦѦ?ӦѦϦ? =1 ʦ = ?ͦ ʦȦŦӦɦ? ӦͦϦ? ̦ Ц?̦ŦӦѦ . ? ʦӦͦϦ? Ӧ? ӦԦ֦?? ̦ŦӦ¦˦Ǧ?? ЦϦ ʦϦ˦ϦԦȦ? ӦǦ ʦӦͦϦ? ?̦̦(=/2,=1/2), ӦԦ?ƦŦӦ ̦ ӦǦ ʦӦͦϦ? 2 () ̦ɦ ̦ ѦͦǦӦɦ? ӦԦ֦? ̦ŦӦ¦˦Ǧ? ʦϦ˦ϦԦ? ӦǦ ʦӦͦϦ? ?̦̦, ?Ӧ ҦԦ?ѦӦǦҦ ЦԦʦ?ӦǦӦ?-ЦɦȦ?ӦǦӦ? (Probability-Density Function) Ӧ? Ȧ ?ͦ: ?( ?) = ? ? ?(?) ? ??1 ????
- 3. ?ЦϦ () ҦԦ?ѦӦǦҦ ?̦̦, ϦЦ? Ϧ?ƦŦӦ ?: ?( ?) = ? ??1 ??? ?? 0 Ԧ?ѦӦǦҦ ?̦̦, ЦѦϦԦҦ?ƦŦ ?ЦϦɦϦ? ЦϦ? ҦǦ̦ͦӦɦ?? ɦĦ?ӦǦӦ?, ЦϦ ʦȦɦҦӦ? ӦϦ ԦЦϦ˦ϦæɦҦ? Ӧ? ̦ɦ ?ʦϦ˦ ĦɦĦɦʦ?. ŦѦɦ?? ? Ԧ?? ?ͦ: ? ?( ?) = ( ? ? 1)!, ??? ???? ? ?????? ?????? ? ?(1) = 1 ? ?( ? + 1) = ??(?) ? ? ( 1 2 ) = ? ҦǦ̦ŦɦئȦ? Ц? ĦŦ Ԧ?Ѧ֦Ŧ ʦ˦ŦɦҦ?? ?Ц? æɦ ӦϦ ԦЦϦ˦ϦæɦҦ? Ӧ? ҦԦ?ѦӦǦҦ? ʦӦͦϦ?? (Cumulative-Density Function) Ӧ? ӦͦϦ?? ?̦̦ æɦ ̦ ?Ѧɦ? Ӧɦ?? ӦϦ . ѦϦЦϦæŦͦ?ҦӦѦɦ ҦԦ?ѦӦǦҦ (t) Ϧ?ƦŦӦ ? (t) = ( ? ? ? 1 ) ? Ŧ? ?Ҧ Ӧɦ? Ӧ? ʦӦͦϦ?? ?̦̦ Ϧ?ƦŦӦ ?: ?( ?) = ??( ?) ?? = ? ? ? ?(?) 0 ? ??1 0 ???? ?? = ? ? ʦ Ħɦ?̦ͦҦ Ӧ? ʦӦͦϦ?? ?ͦ : ?( ?) = ? ?2 ӦͦϦ? ?̦̦ ¦?ҦʦŦ ЦϦ˦?? ŦզѦ̦Ϧ?? Ҧ ЦϦ˦?? ŦЦɦҦ?̦? ʦ ЦŦ?. ɦ ҦԦæʦŦʦѦɦ?ͦ: ? ӦǦ ͦ˦ϦæɦҦӦɦ? ŦЦɦҦ?̦, ?ЦϦ ̦ϦͦӦŦ˦ϦЦϦɦ?ͦӦ Ϧ Цɦ?ҦŦ? Ŧ?? ֦ѦӦϦզԦ˦?Ϧ ̦ɦ? Ҧզ˦ɦҦӦɦ?? ŦӦɦ??
- 4. ? Ӧ? ŦԦѦϦŦЦɦҦ?̦? (ʦ ҦӦϦ ͦŦϦ?ҦӦӦ ʦ?Ħ Ӧ? ŦԦѦϦҦӦӦɦҦӦɦ??), ?ЦϦ ֦ѦǦҦɦ̦ϦЦϦɦ?Ӧ æɦ ӦǦ ЦŦѦɦæѦ? Ӧئ ֦?ͦئ ?ʦѦɦҦ? Ӧئ ͦŦԦ?ͦئ ? Ӧ ŦͦŦӦɦ?, ֦ѦǦҦɦ̦ϦЦϦɦ?Ӧ ҦӦǦ ЦŦѦɦæѦ? Ӧ? ¦ʦӦǦѦɦ?? ?ʦզѦҦ? Ŧ?? æϦͦɦ?Ϧ (?ЦϦ Ц?̦ŦӦѦ? ĦǦ?ͦŦ ӦϦ ?Ҧ ѦɦȦ? Ŧʦ?ΦŦئ ?ʦ˦ ʦ Ӧ Ӧ ?Ҧ ѦɦȦ? ЦѦئӦ?? ЦϦ Ц?æϦͦӦ ? ?ͦ mRNA) ? Ӧ Ŧئ? Ԧ?, ?ЦϦ ֦ѦǦҦɦ̦ϦЦϦɦ?Ӧ Ҧ ̦Ϧͦ?˦ æɦ ӦǦ ЦŦѦɦæѦ? ϦԦ? ̦ͦϦ?? ? Ӧ Ц?Ʀɦ? ӦӦɦҦӦɦ?, զ? ֦ѦǦҦɦ̦ϦЦϦɦ?Ӧ ? Ŧ Ӧئ ЦѦϦ?Ѧئ ʦӦͦϦ? (prior distribution) Ҧ ̦Ϧͦ?˦ ?ЦϦ Ŧ Ӧئ ԦҦ?Ѧئ ʦӦͦϦ? (posterior distribution) ?ͦ ʦӦͦϦ? Poisson ? ?̦̦ ? Ӧ ӦӦɦҦӦɦ? ĦѦϦ˦Ϧ?,?ЦϦ Ц?֦Ŧ Ц˦ǦѦϦզϦ?? æɦ Ӧ ?צ? Ӧئ ¦ѦϦ֦ϦЦ?ҦŦئ (Ҧ֦ŦӦɦ? Ц?ĦŦɦæ̦ Ȧ ĦϦȦ? ҦӦ ҦԦ?֦Ŧɦ) ŦѦɦæѦ? ӦϦ ʦɦͦ?ͦϦ ЦϦ˦?? ?Ѧ? Ӧ? զѦɦ?? ЦѦӦǦѦ?ͦӦ ҦԦ֦? զɦ?̦Ŧͦ ˦ŦɦצԦĦ?? ЦϦ ĦǦ̦ɦϦԦѦæ? ӦŦ?ҦӦɦ ЦѦϦ?̦Ӧ ҦӦ? ӦϦЦɦ?? ʦϦɦͦئ??. ?ӦҦ, ?ͦŦӦ ЦѦϦҦ?ȦŦɦ ͦ ?ͦŦ ̦ɦ ̦ϦͦӦŦ˦ϦЦ?ǦҦ ԦӦ? ӦϦ զɦͦϦ?ͦϦ, ̦ ҦʦϦ? ӦǦ ʦ?ӦŦѦ ΦɦϦЦ?ǦҦ ӦϦ ͦŦѦ?, ?Ҧ æɦ ?Ҧ, ?Ҧ ʦ æɦ ѦĦŦԦӦɦ? ֦?Ҧ. Ԧ?, Ϧ ͦ˦Ԧ?? ӦϦ ҦԦæʦŦʦѦɦ?ͦϦ ʦɦͦ?ͦϦ ֦ѦŦ?ƦŦӦ ͦ ʦӦͦ?ҦϦԦ ¦?ӦŦѦ Ӧ ?Ѧ? ʦ Ӧ ҦԦ֦?ӦǦӦ Ŧ̦?ͦɦҦ? Ӧئ ¦ѦϦ֦ϦЦ?ҦŦئ ЦϦ Ȧ ЦѦϦ?צϦԦ. ?˦˦Ǧ˦ ҦӦӦɦҦӦɦ? ̦Ϧͦ?˦, ̦ ĦŦĦϦ?ͦ Ħɦ?Ѧئ ЦŦѦ?Ħئ, ?ͦ ЦϦ? ֦?Ҧɦ̦ ŦѦæ˦? ҦӦ ?Ѧɦ Ӧئ ͦ˦Ԧ?. ӦԦЦɦ? ЦѦϦ?ææɦҦ, ?ӦҦ ?ҦӦ ͦ ?ѦϦԦ̦ Ӧ? ЦѦ?ӦǦӦ? Ц˦ǦѦϦզϦ?? æɦ Ӧ ʦ? ?ЦϦ? Ŧ?ЦŦĦ Ӧئ ¦ѦϦ֦ϦЦ?ҦŦئ, ?ͦ ?Ҧ ? Ӧ ɦҦӦϦѦɦ? ҦӦϦɦ֦? Ӧئ ¦ѦϦ֦ϦЦ?ҦŦئ. Ԧ? Ӧ ҦӦϦɦ֦? ¦ϦǦȦ? ӦϦ? ͦ˦Ԧ?? ӦϦ ʦɦͦ?ͦϦ ͦ ?֦ϦԦ ̦ɦ æŦͦɦ? ɦ? æɦ Ӧ ?צ?, Ӧ ֦?ͦ ʦ Ӧ ?Ѧ Ӧئ ¦ѦϦ֦ϦЦ?ҦŦئ. ?ͦǦȦ? զɦ?̦Ŧͦ ЦϦӦŦ˦? (ϦѦɦҦ?ͦ? զϦ??) ?˦˦Ŧɦצ ҦӦϦɦ֦?ئ ?ЦϦɦئ ЦŦѦɦϦ? , ?æ ̦ ʦѦɦ¦?? ? Ǧ̦ɦӦŦ˦?? ?ѦŦԦͦ?. ?Ҧ ҦӦϦɦ֦? Ħɦ?ӦŦ ͦ˦Ԧ??, ʦ ̦ Ӧ ֦?Ҧ Ӧئ ʦ?˦ئ ЦѦ̦ŦӦѦɦ? ҦӦӦɦҦӦɦ? ̦Ϧͦ?˦ئ, ̦ЦϦѦ? ͦ ŦʦӦɦ?ҦŦ ӦǦ ?ͦӦҦ Ӧ?
- 5. ¦ѦϦ?ЦӦئҦ?. Ԧ? ̦ЦϦѦ? ͦ ?ͦŦ Ҧ Ǧ̦Ŧ?Ҧɦ, ̦Ǧͦɦ? ? Ŧ?Ҧɦ ?Ҧ, ?˦Ϧæ ̦ Ӧ ĦŦĦϦ?ͦ ЦϦ ?֦Ŧ ҦԦ˦?ΦŦ. ? ʦӦ˦˦Ǧ?ӦŦѦ ̦Ϧͦ?˦1 æɦ ӦǦ ЦŦѦɦæѦ? ӦϦ ҦԦæʦŦʦѦɦ?ͦϦ ʦɦͦ?ͦϦ, ?֦Ŧ ЦϦĦŦɦ֦Ȧ? ӦͦϦ? ?̦̦. ӦͦϦ? ?̦̦ ? ̦Ϧͦ?˦ Ŧʦ?̦ǦҦ? ӦϦ ʦɦͦ?ͦϦ Ӧ? ˦ŦɦצԦĦ?? (ѦɦȦ̦ǦӦɦ? զѦ̦Ϧ?) ӦǦ ЦѦ??ȦŦҦ Ц? ?֦Ŧ ?ͦŦ ҦԦ˦˦Ϧ? Ӧئ ЦѦ?Ӧئ ĦŦĦϦ?ͦئ, ͦ˦Ԧ?? Ȧ ΦŦʦɦ?ҦŦ ӦǦ ΦɦϦЦ?ǦҦ ӦϦ? ̦ ҦʦϦ? ͦ Ŧ?æŦ ֦?Ҧɦ̦ ҦԦ̦ЦŦ?Ҧ̦Ӧ. 2014, ʦ? ?Ҧ ?Ѧ, ҦǦ̦Ŧ?ȦǦʦ Ӧ Ŧ?? ?צ ¦ѦϦ֦ϦЦ?ҦŦئ (Ҧ mm) ?Ȧ ?ͦ, ҦӦǦ ?˦ Johannesburg. 4 , 6 , 27 , 7 , 11 , 103 , 125 , 94, 90 , 54 , 13 , 9 ɦ ͦ ?ͦŦ ֦?Ҧ ӦϦ ̦Ϧͦ?˦Ϧ Ӧ? ?̦̦ ӦͦϦ??, Ц?ЦŦ Ц?Ӧ ͦ ŦʦӦɦ̦ǦȦ? Ϧ Ц?̦ŦӦѦϦ ʦ ,?Ҧ ? Ӧ Ħɦ?Ҧɦ̦ ĦŦĦϦ?ͦ. Ӧ ֦?Ҧ Ӧئ ̦Ŧ?Ħئ ?æɦҦӦ? ɦȦͦϦ?ͦŦɦ?2 , Ϧ ŦʦӦɦ?ҦŦ? æɦ Ӧ ʦ ?ͦ Ϧ Ŧ??: =0.7532 & =60.0723 ?ҦӦ ӦԦ֦? ̦ŦӦ¦˦Ǧ? ϦЦ? ЦŦѦɦæ?զŦ Ӧ ?צ? Ӧ? ¦ѦϦ?ЦӦئҦ? ЦϦ ҦǦ̦Ŧ?ȦǦʦ ҦӦǦ ЦŦѦɦϦ? ӦϦ Johannesburg Ӧ 2014. ?ӦҦ, ?̦զئͦ ̦ Ӧ ЦѦ?ͦ ҦӦϦɦ֦?: ?~?????(? = 0.7532 , ? = 60,0723) ɦҦ?æѦ̦̦ Ӧ? ҦԦæʦŦʦѦɦ?ͦ? ʦӦͦϦ?? ?ͦ: 1 ҦԦæʦŦʦѦɦ?ͦ ʦӦͦϦ?, ЦѦϦӦɦ?Ӧ ? Ц?̦Ϧɦ? ʦӦͦϦ?? ̦ ¦Ѧ? ĦŦΦ? ϦԦ? (Weibull, Lognormal) ?æ Ӧ? Ц?ӦǦӦ? Ӧئ ԦЦϦ˦ϦæɦҦ? Ӧ? 2 ԦЦϦ˦ϦæɦҦ̦? ЦѦ˦?ЦϦͦӦ æɦ ?æϦ? ЦѦʦӦɦ?ӦǦӦ?
- 6. ҦǦ̦ŦɦئȦ? Ц? Ӧ ɦҦ?æѦ̦̦ ?ͦ Ц?̦Ϧɦ ̦ Ӧ ɦҦ?æѦ̦̦ Ӧ? ʦȦŦӦɦ?? ӦͦϦ?? ̦ Ц?̦ŦӦѦ =60,0723. Ԧ? ҦԦ̦¦?ͦŦ ?æ ӦϦ ?Ӧ Ц?̦ŦӦѦ? ЦѦϦҦŦҦŦæ?ƦŦ Ӧ ̦Ϧ?Ħ. ?̦զئͦ ̦ Ҧ֦ŦӦɦ?? ̦Ŧ?Ӧ?, Ӧ ɦĦͦɦ? ?צ? ¦ѦϦ?ЦӦئҦ? (?ӦҦ ?ҦӦ ͦ ̦Ǧ ҦǦ̦ŦɦئȦ? ?Ӧ Ц?¦˦Ǧ̦ ?˦˦Ŧɦצ?, ˦? ?Ӧ ʦ Ц?¦˦Ǧ̦ ԦЦŦѦ֦?˦ǦҦ?) æɦ ?ЦϦɦ ҦԦæʦŦʦѦɦ?ͦ ?ͦ ?ͦ ̦ŦӦ? 40 ʦ 100 mm/?ͦ. ?ӦҦ, ЦɦȦ?ӦǦӦ ?ͦ? ?ͦ? ӦϦ Ŧ?̦ŦͦϦ ?ӦϦ? ͦ ЦѦϦԦҦ?ҦŦ ˦ŦɦצԦĦ? ?ͦ: ?( ? 10) = ?(10) = 0.2625 = 26.25% ͦ?ȦŦӦ, ЦɦȦ?ӦǦӦ ͦ Ԧ?ѦΦŦ ¦ѦϦ? ̦Ŧæ?ӦŦѦ? ?ͦӦҦ? ? ?Ӧ ̦ЦϦѦ? Ӧ ӦϦЦɦ? ҦԦҦ?̦Ӧ ?ĦѦŦԦҦ? ͦ ͦ?ΦϦԦ ?ͦ: ?( ? > 100) = 1 ? ?(100) = 0.1237 = 12.37% ҦԦͦϦ˦ɦ? ЦɦȦ?ӦǦӦ ʦѦ?ئ ŦͦĦŦ֦Ϧ?ͦئ ҦӦǦ ЦŦѦɦϦ?, ?ͦ: ?( ? 10) + ?( ? > 100) = 0.2625 + 0.1237 = 0.3862 = 38.62% ҦԦ̦?ѦҦ̦ ? ӦǦ ЦѦ?ͦ ̦ϦͦӦŦ˦ϦЦ?ǦҦ ?ͦ ?Ӧ ?Ҧ ҦӦϦ Ŧ?̦Ŧͦ ֦?ͦ, (ЦŦ?ЦϦ) 1 ҦӦϦ? 3 ?ͦ? Ȧ ЦѦϦԦҦ?ҦϦԦ ?ЦϦɦ ʦѦ? զɦ?̦Ŧͦ ˦ŦɦצԦĦ?? ? ?ͦӦϦͦ? ¦ѦϦ?ЦӦئҦ?. Ԧ? ?ͦŦ Ӧ ĦԦͦ?ӦǦӦ ҦӦ? ӦϦЦɦ?? Ѧ?? ͦ Ц?ΦϦԦ ͦ?æ? ʦ ͦ ʦӦҦʦŦ?ҦϦԦ Ӧ ЦѦ?ӦǦӦ ?ӦѦ, ?ӦҦ ?ҦӦ ͦ ŦΦ˦ŦɦզȦ? ŦͦӦ?? ?ͦĦԦͦ?.
- 7. ͦզϦ??-ɦ¦˦ɦϦæѦ? ? Wikipedia.org ? Use of the gamma distribution to represent monthly rainfall In Africa for drought monitoring applications, Gregory J. Husak, Joel Michaelsen and Chris Funk, 2005 ? Johannesburg.climatemps.com