《概率統(tǒng)計(jì)》 課件 7.1 點(diǎn)估計(jì)

概率統(tǒng)計(jì)0102估計(jì)量的評(píng)選標(biāo)準(zhǔn)點(diǎn)估計(jì)第七章參數(shù)估計(jì)03區(qū)間估計(jì)統(tǒng)計(jì)推斷是依據(jù)從總體中抽取的一個(gè)簡單隨機(jī)樣本對(duì)總體進(jìn)行分析和推斷的.統(tǒng)計(jì)推斷的基本問題可分為兩類：一類是參數(shù)估計(jì)問題，另一類是假設(shè)檢驗(yàn)問題。本章先介紹參數(shù)估計(jì).概率論與數(shù)理統(tǒng)計(jì)背景§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)背景§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)背景§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)參數(shù)估計(jì)分為點(diǎn)估計(jì)和區(qū)間估計(jì)兩類.本章第一節(jié)先介紹點(diǎn)估計(jì)的基本知識(shí)，第二節(jié)介紹估計(jì)量的評(píng)價(jià)標(biāo)準(zhǔn)，第三節(jié)介紹區(qū)間估計(jì).概率論與數(shù)理統(tǒng)計(jì)背景§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)概率論與數(shù)理統(tǒng)計(jì)概念

§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)參數(shù)估計(jì)就是利用樣本值對(duì)總體的未知參數(shù)作出的估計(jì)。概率論與數(shù)理統(tǒng)計(jì)例

概念§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)概率論與數(shù)理統(tǒng)計(jì)解

概念§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)解

概念§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)概率論與數(shù)理統(tǒng)計(jì)定義

概念§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)概念§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)矩法是由統(tǒng)計(jì)學(xué)家皮爾遜在19世紀(jì)末20世紀(jì)初引入的，它是較早被提出的求參數(shù)點(diǎn)估計(jì)的一種方法。在統(tǒng)計(jì)學(xué)中，矩是指以數(shù)學(xué)期望為基礎(chǔ)而定義的隨機(jī)變量的數(shù)字特征，一般分為原點(diǎn)矩和中心矩，記：概率論與數(shù)理統(tǒng)計(jì)矩估計(jì)法§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)矩估計(jì)法§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)矩估計(jì)法§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)矩估計(jì)法§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)概率論與數(shù)理統(tǒng)計(jì)定義

矩估計(jì)法§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)概率論與數(shù)理統(tǒng)計(jì)例

矩估計(jì)法§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)概率論與數(shù)理統(tǒng)計(jì)解

矩估計(jì)法§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

樣本均值

，

概率論與數(shù)理統(tǒng)計(jì)解

矩估計(jì)法§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

由題中給出的樣本觀測(cè)值得

概率論與數(shù)理統(tǒng)計(jì)例

矩估計(jì)法§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)概率論與數(shù)理統(tǒng)計(jì)解

矩估計(jì)法§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)例

矩估計(jì)法§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)概率論與數(shù)理統(tǒng)計(jì)解

矩估計(jì)法§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)概率論與數(shù)理統(tǒng)計(jì)解矩估計(jì)法§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)解矩估計(jì)法§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

解得概率論與數(shù)理統(tǒng)計(jì)注對(duì)于任意分布，只要總體均值及方差存在，其均值和方差的矩估計(jì)量表達(dá)式都是一樣的，總體均值和方差的矩估計(jì)量分別是樣本均值和樣本的二階中心矩。矩估計(jì)法§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)概率論與數(shù)理統(tǒng)計(jì)例

矩估計(jì)法§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)概率論與數(shù)理統(tǒng)計(jì)解由于矩估計(jì)法§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)解矩估計(jì)法§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)解

矩估計(jì)法§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)說明綜合以上關(guān)于矩法的討論，我們將利用矩法求點(diǎn)估計(jì)的步驟總結(jié)如下：矩估計(jì)法§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)說明

矩估計(jì)法§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)說明

矩估計(jì)法§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)說明

矩估計(jì)法§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)下面，我們從一個(gè)例子出發(fā)，來說明極大似然估計(jì)的基本思想。極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)概率論與數(shù)理統(tǒng)計(jì)例

極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)概率論與數(shù)理統(tǒng)計(jì)解極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)解極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)解極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)從而有

概率論與數(shù)理統(tǒng)計(jì)注極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)這里注意到：

概率論與數(shù)理統(tǒng)計(jì)解極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

因此，我們更有理由認(rèn)為這張靶紙是射手乙所射，即

概率論與數(shù)理統(tǒng)計(jì)這種以最大概率對(duì)參數(shù)做出估計(jì)的方法稱為極大似然估計(jì)法。這種思想就是極大似然思想。極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)下面我們分別對(duì)離散型總體和連續(xù)型總體來闡述極大似然估計(jì)法。極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)概率論與數(shù)理統(tǒng)計(jì)

極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)

極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)概率論與數(shù)理統(tǒng)計(jì)

極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)概率論與數(shù)理統(tǒng)計(jì)

定義極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)概率論與數(shù)理統(tǒng)計(jì)

注極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)

例極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)構(gòu)造似然函數(shù)解極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)兩邊取對(duì)數(shù)，得

概率論與數(shù)理統(tǒng)計(jì)

解極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)

解極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)

例極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)概率論與數(shù)理統(tǒng)計(jì)

解極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)解極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)兩邊取對(duì)數(shù)，得

概率論與數(shù)理統(tǒng)計(jì)兩邊求導(dǎo)，并令導(dǎo)數(shù)為零，得解極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)解得

概率論與數(shù)理統(tǒng)計(jì)解極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)例極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)

解極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)構(gòu)造似然函數(shù)解極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)對(duì)上式兩邊取對(duì)數(shù)解極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)

解極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)解得解極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)

解極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)注

極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)概率論與數(shù)理統(tǒng)計(jì)例

極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)概率論與數(shù)理統(tǒng)計(jì)

解極大似然估計(jì)§7.

1點(diǎn)估計(jì)背景及概念矩估計(jì)法極大似然估計(jì)

概率論與數(shù)理統(tǒng)計(jì)

解極大似然估計(jì)§7.

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