# The Combined-Unified Hybrid Censored Samples from Pareto Distribution: Estimation and Properties
## 6 Conclusions  
In this paper, MLEs and the Bayesian estimates of the unknown parameters from Pareto distribution under C-UHCS\((m,l;t_{1},t_{2})\) model are obtained. Some efficiency properties of the MLEs estimate are discussed, including, the unbiasedness, minimum variance unbiased estimate and sufficiency. MCMC technique is used to carry out the Bayesian estimates. The interval estimates are developed using the observed Fisher information  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{\(\boldsymbol{T}\)} & \multicolumn{2}{c}{**Point Estimation**} & \multicolumn{4}{c}{**Interval Estimation**} \\ \hline  & & **MLE** & **Bayes** & \multicolumn{2}{c}{**MLE**} & \multicolumn{2}{c}{**Bayes**} \\ \hline  & & & & **95\%** & **90\%** & **95\%** & **90\%** \\ \hline \(X_{m-5,15}=1.28\) & \(k\) & 0.976 & 1.042 & 0.818 1.134 & 0.843 1.109 & 0.963 1.075 & 0.980 1.074 \\  & 0.081 & 0.066 & 0.317 & 0.267 & 0.112 & 0.094 \\  & \(\alpha\) & 2.962 & 2.963 & 1.792 4.132 & 1.977 3.947 & 2.867 3.057 & 2.872 3.052 \\  & & 0.597 & 0.841 & 2.340 & 1.970 & 0.190 & 0.180 \\  & \(R(. )\) & 0.223 & 0.271 & 0.000 0.485 & 0.002 0.444 & 0.213 0.303 & 0.225 0.301 \\  & \(\alpha\) & 0.134 & 0.841 & 0.485 & 0.337 & 0.090 & 0.076 \\  & \(H(. )\) & 1.828 & 1.829 & 0.845 28.121 & 1.001 2.656 & 1.770 1.887 & 1.773 1.884 \\  & & 0.502 & 0.841 & 1.444 & 1.216 & 0.117 & 0.111 \\ \hline \(X_{l-7,15}=1.33\) & \(k\) & 0.983 & 1.056 & 0.831 1.135 & 0.855 1.111 & 0.991 1.082 & 1.007 1.082 \\  & 0.077 & 0.077 & 0.303 & 0.255 & 0.091 & 0.075 \\  & \(\alpha\) & 3.730 & 3.732 & 2.402 5.058 & 2.612 4.848 & 3.635 3.825 & 3.640 3.820 \\  & \(R(. )\) & 0.678 & 0.091 & 2.656 & 2.236 & 0.190 & 0.180 \\  & \(R(. )\) & 0.155 & 0.203 & 0.025 0.285 & 0.046 0.265 & 0.159 0.227 & 0.169 0.225 \\  & \(0.066 & 0.091 & 0.309 & 0.260 & 0.068 & 0.056 \\  & \(H(. )\) & 2.302 & 2.303 & 1.175 3.430 & 1.353 3.251 & 2.244 2.361 & 2.247 2.358 \\  & \(0.575 & 0.091 & 1.640 & 1.830 & 0.117 & 0.111 \\ \hline \(X_{l-9,15}=1.59\) & \(k\) & 0.984 & 1.059 & 0.813 1.155 & 0.840 1.128 & 0.998 1.083 & 1.012 1.083 \\  & & 0.087 & 0.079 & 0.341 & 0.287 & 0.085 & 0.071 \\  & \(\alpha\) & 3.869 & 3.872 & 2.477 5.260 & 2.697 5.040 & 3.774 3.964 & 3.780 3.959 \\  & \(\alpha\) & 0.710 & 0.091 & 2.783 & 2.343 & 0.190 & 0.180 \\  & \(R(. )\) & 0.145 & 0.193 & 0.042 0.249 & 0.058 0.233 & 0.153 0.215 & 0.161 0.213 \\  & & 0.053 & 0.091 & 0.291 & 0.245 & 0.062 & 0.052 \\  & \(H(. )\) & 2.388 & 2.390 & 1.175 3.601 & 1.367 3.410 & 2.330 2.447 & 2.333 2.444 \\  & & 0.619 & 0.091 & 1.718 & 1.446 & 0.117 & 0.111 \\ \hline \(t_{1}=1.3,D=6\) & \(k\) & 0.980 & 1.050 & 0.827 1.134 & 0.851 1.109 & 0.979 1.079 & 0.996 1.078 \\  & & 0.078 & 0.072 & 0.307 & 0.259 & 0.100 & 0.083 \\  & \(\alpha\) & 3.379 & 3.380 & 2.123 4.635 & 2.321 4.437 & 3.285 3.474 & 3.290 3.469 \\  & & 0.641 & 0.426 & 2.513 & 2.115 & 0.189 & 0.179 \\  & \(R(. )\) & 0.183 & 0.232 & 0.007 0.359 & 0.035 0.331 & 0.181 0.259 & 0.192 0.257 \\  & \(0.089 & 0.426 & 0.349 & 0.294 & 0.078 & 0.064 \\  & \(H(. )\) & 2.086 & 2.086 & 1.025 3.146 & 1.193 2.979 & 2.028 2.144 & 2.031 2.141 \\  & & 0.541 & 0.426 & 1.551 & 1.306 & 0.117 & 0.111 \\ \hline \(t_{2}=1.4,D=8\) & \(k\) & 0.983 & 1.058 & 0.822 1.145 & 0.848 1.1119 & 0.995 1.083 & 1.010 1.082 \\  & \(\alpha\) & 0.082 & 0.078 & 0.323 & 0.272 & 0.087 & 0.072 \\  & \(\alpha\) & 3.802 & 3.805 & 2.442 51.62 & 2.657 49.47 & 3.707 3.897 & 3 matrix and MCMC. The theoretical findings of the paper are applied to analyze a real dataset under different choices of the censoring. The numerical results show the efficiency performance of the proposed model. Finally, the proposed censoring model has flexible futures to switch between Type-I and Type-II censoring according the experiments need. Conceptualization, K.S.S., W.E. ; methodology, K.S.S., W.E. ; software, W.E. ; validation and formal analysis, K.S.S. ; resources, K.S.S., W.E. ; writing--original draft preparation, W.E. ; writing--review and editing, K.S.S., W.E.