id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
iajs-2946	Rasheed, Huda Abdullah; N. Abd, Maryam 	Bayesian Estimation for Two Parameters of Exponential Distribution under Different Loss Functions	2023	12	.pdf	application/pdf	4052	175	68	Based on the precautionary loss function, the risk function RP(γ̂, γ) can be derived as follows: RP(γ̂, γ) = E[L(γ̂, γ)] = ∫ L(γ̂, γ) h(γ|x)dγ ∞ 0 RP(γ̂, γ) = ∫ (γ − γ̂)2 γ̂ ∞ 0 h(γ|x)dγ = ∫ (γ2γ̂−1) h(γ|x)dγ − ∫ 2γ h(γ|x)dγ ∞ 0 + ∫ γ̂ ∞ 0 ∞ 0 h(γ|x)dγ RP(γ̂, γ) = E(γ2|x)γ̂−1 − 2E(γ|x) + γ̂. Taking the partial derivative for RP(γ̂, γ) with respect to γ̂ and setting it equal to zero yields: −E(γ2|x)γ̂−2 + 1 = 0. Therefore, the Tierney-Kadane approximation will be used as follows: 𝑙𝑛𝐽(𝛾, 𝛿) = 𝑙𝑛𝑐 − 𝑐 𝛾 + 𝑎𝑙𝑛𝑏 + (𝑎 − 1) 𝑙𝑛𝛿	cache/iajs-2946.pdf	txt/iajs-2946.txt