Ordering results for random maxima and minima from two dependent Kumaraswamy generalized distributed samples
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| Format: | Preprint |
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2025
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| _version_ | 1866909745509564416 |
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| author | Das, Sangita Balakrishnan, Narayanaswamy |
| author_facet | Das, Sangita Balakrishnan, Narayanaswamy |
| contents | Let $\{X_{1},\ldots,X_{N_1}\}$ and $\{Y_{1},\ldots,Y_{N_2}\}$ be two sequences of interdependent heterogeneous samples, where for $i=1,\ldots,N_{1},$ $X_{i}\sim \text{Kw-G}(x, α_{i}, γ_{i};G)$ and for $i=1,\ldots,N_{2},$ $Y_{i}\sim \text{Kw-G}(x, β_{i}, δ_{i};H),$ where $G$ and $H$ are baseline distributions in the Kumaraswamy generalized model and $N_1$ and $N_2$ are two positive integer-valued random variables, independently of $X_{i}'$s and $Y_{i}'$s, respectively. In this article, we establish several stochastic orders such as usual stochastic, hazard rate, reversed hazard rate, dispersive and likelihood ratio orders between the random maxima ($X_{{N_1}:{N_1}}$ and $Y_{{N_2}:{N_2}}$) and the random minima ($X_{{1}:{N_1}}$ and $X_{{1}:{N_2}}$), when the sample sizes are different and random (positive). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14855 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ordering results for random maxima and minima from two dependent Kumaraswamy generalized distributed samples Das, Sangita Balakrishnan, Narayanaswamy Statistics Theory Let $\{X_{1},\ldots,X_{N_1}\}$ and $\{Y_{1},\ldots,Y_{N_2}\}$ be two sequences of interdependent heterogeneous samples, where for $i=1,\ldots,N_{1},$ $X_{i}\sim \text{Kw-G}(x, α_{i}, γ_{i};G)$ and for $i=1,\ldots,N_{2},$ $Y_{i}\sim \text{Kw-G}(x, β_{i}, δ_{i};H),$ where $G$ and $H$ are baseline distributions in the Kumaraswamy generalized model and $N_1$ and $N_2$ are two positive integer-valued random variables, independently of $X_{i}'$s and $Y_{i}'$s, respectively. In this article, we establish several stochastic orders such as usual stochastic, hazard rate, reversed hazard rate, dispersive and likelihood ratio orders between the random maxima ($X_{{N_1}:{N_1}}$ and $Y_{{N_2}:{N_2}}$) and the random minima ($X_{{1}:{N_1}}$ and $X_{{1}:{N_2}}$), when the sample sizes are different and random (positive). |
| title | Ordering results for random maxima and minima from two dependent Kumaraswamy generalized distributed samples |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2508.14855 |