Sampling theorem and efficiency comparison of three local minimum variance unbiased estimators of the mean and variance of the exponential distribution

Figures & data

Table 1. Variance comparison of three local minimum variance unbiased estimators of expectation under small sample

$n$	$2$	$3$	$4$	$5$	$6$
$D{\hat{\alpha }}_0$	$0.5$	$0.3333$	$0.25$	$0.2$	$0.1667$
$D{\hat{\alpha }}_1$	$0.5$	$0.3572$	$0.2883$	$0.2470$	$0.2192$
$D{\hat{\alpha }}_2$	$0.5$	$0.4048$	$0.3500$	$0.3130$	$0.2858$
$\cdot \cdot \cdot \cdot \cdot \cdot$	$46$	$47$	$48$	$49$	$50$	$\cdot \cdot \cdot \cdot \cdot \cdot$
$\cdot \cdot \cdot \cdot \cdot \cdot$	$0.0217$	$0.0213$	$0.0208$	$0.0204$	$0.0200$	$\cdot \cdot \cdot \cdot \cdot \cdot$
$\cdot \cdot \cdot \cdot \cdot \cdot$	$0.0775$	$0.0768$	$0.0761$	$0.0756$	$0.0751$	$\cdot \cdot \cdot \cdot \cdot \cdot$
$\cdot \cdot \cdot \cdot \cdot \cdot$	$0.1107$	$0.1097$	$0.1087$	$0.1078$	$0.1069$	$\cdot \cdot \cdot \cdot \cdot \cdot$

Table 2. Variance comparison of three local minimum variance unbiased estimators of variance under small sample

$n$		$2$		$3$		$4$		$5$		$6$
$D{\hat{\lambda }}_0$		$2.5$		$1.5909$		$1.1538$		$0.9016$		$0.7386$
$D{\hat{\lambda }}_1$		$2.5$		$1.7932$		$1.4490$		$1.2415$		$1.1010$
$D{\hat{\lambda }}_2$		$2.5$		$2.1063$		$1.8391$		$1.6487$		$1.5407$
$\cdot \cdot \cdot \cdot \cdot \cdot$	$46$		$47$		$48$		$49$		$50$		$\cdot \cdot \cdot \cdot \cdot \cdot$
$\cdot \cdot \cdot \cdot \cdot \cdot$	$0.0883$		$0.0864$		$0.0845$		$0.0828$		$0.0811$		$\cdot \cdot \cdot \cdot \cdot \cdot$
$\cdot \cdot \cdot \cdot \cdot \cdot$	$0.3783$		$0.3748$		$0.3714$		$0.3682$		$0.3751$		$\cdot \cdot \cdot \cdot \cdot \cdot$
$\cdot \cdot \cdot \cdot \cdot \cdot$	$0.5573$		$0.5520$		$0.5468$		$0.5418$		$0.5369$		$\cdot \cdot \cdot \cdot \cdot \cdot$