Analysis of Climatic Change through Comparing Methods of Statistical Estimation for Two-Parameter Gamma Distribution in Nigeria

Aliu A. Hassan
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Abstract

In other to improve the ability of decisionmakers to prepare for and deal with the unforeseen circumstances resulting from climate change as consequences of precipitation fluctuations, extreme and torrential rainfall. It is important to provide a more complete understanding of the range and likelihood of rainfall patterns a location could receive using a probabilistic model whose parameters might complement or even replace such common measures as the mean, median, variance, minimum, maximum and quartile values as major descriptors of rainfall at such location. Daily precipitation totals can be approximated by the gamma distribution as it is bounded on the left at zero and positively skewed indicating an extended tail to the right which suit the distribution of daily rainfall and accommodate the lower limit of zero which constrains rainfall values. This paper presents the comparison between Maximum Likelihood Estimation (MLE) of closed & open form solutions and Method of Moment Estimation (MME) of location and scaling parameters of the twoparameter gamma distribution, the parameters were estimated using MME and MLE with their performance adjudged and the result obtained showed that the closedform solution of the MLE outperformed the open form solution and MME by comparing their estimates for the scaling parameter.
尼日利亚两参数伽玛分布统计估计方法比较分析气候变化
另一方面,提高决策者的能力,以防备和处理由于降水波动、极端和暴雨造成的气候变化所造成的不可预见情况。重要的是要更全面地了解一个地点可能接收到的降雨模式的范围和可能性,使用概率模型,其参数可以补充甚至取代作为该地点降雨主要描述符的平均值、中位数、方差、最小值、最大值和四分位数值等常用度量。日降水总量可以用伽马分布来近似,因为它在左侧以零为界,正向倾斜,表明向右延伸的尾巴适合日降雨量的分布,并容纳限制降雨量值的零的下限。本文将封闭和开放形式解的最大似然估计(MLE)与双参数伽玛分布的位置和尺度参数的矩估计方法(MME)进行了比较,分别使用MME和MLE对参数进行了估计,并对其性能进行了评价,通过对尺度参数的估计比较,结果表明MLE的封闭形式解优于开放形式解和MME。
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