Knowledge (XXG)

Poisson sampling

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Ghosh, Dhiren, and Andrew Vogt. "Sampling methods related to Bernoulli and Poisson Sampling." Proceedings of the Joint Statistical Meetings. American Statistical Association Alexandria, VA, 2002.
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th element of the population that is sampled is included in a sample during the drawing of a single sample is denoted by
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Each element of the population may have a different probability of being included in the sample (
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and the second-order inclusion probability that a pair consisting of the
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which determines whether the element becomes part of the sample.
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The following relation is valid during Poisson sampling when
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Carl-Erik Sarndal; Bengt Swensson; Jan Wretman (1992).
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th element of the population is denoted by the symbol
328: 298: 237: 208: 175: 140: 93: 59: 341: 314: 283:{\displaystyle \pi _{ij}=\pi _{i}\times \pi _{j}.} 282: 220: 191: 153: 106: 72: 122:A mathematical consequence of Poisson sampling 471: 391: 389: 8: 478: 464: 333: 327: 303: 297: 271: 258: 242: 236: 207: 180: 174: 145: 139: 98: 92: 64: 58: 385: 7: 432: 430: 450:. You can help Knowledge (XXG) by 39:process where each element of the 14: 434: 126:Mathematically, the first-order 398:Model Assisted Survey Sampling 1: 518: 429: 15: 315:{\displaystyle \pi _{ii}} 192:{\displaystyle \pi _{ij}} 342:{\displaystyle \pi _{i}} 154:{\displaystyle \pi _{i}} 73:{\displaystyle \pi _{i}} 16:Not to be confused with 221:{\displaystyle i\neq j} 446:-related article is a 343: 316: 284: 222: 193: 155: 108: 74: 31:(sometimes denoted as 344: 317: 285: 223: 194: 156: 128:inclusion probability 109: 107:{\displaystyle p_{i}} 84:inclusion probability 75: 18:Poisson disk sampling 364:Poisson distribution 326: 296: 235: 206: 173: 138: 91: 57: 497:Sampling techniques 43:is subjected to an 359:Bernoulli sampling 339: 312: 280: 218: 189: 151: 116:Bernoulli sampling 104: 70: 25:survey methodology 459: 458: 407:978-0-387-97528-3 322:is defined to be 87:of that element ( 509: 502:Statistics stubs 480: 473: 466: 438: 431: 424: 418: 412: 411: 393: 348: 346: 345: 340: 338: 337: 321: 319: 318: 313: 311: 310: 289: 287: 286: 281: 276: 275: 263: 262: 250: 249: 227: 225: 224: 219: 198: 196: 195: 190: 188: 187: 160: 158: 157: 152: 150: 149: 113: 111: 110: 105: 103: 102: 79: 77: 76: 71: 69: 68: 29:Poisson sampling 517: 516: 512: 511: 510: 508: 507: 506: 487: 486: 485: 484: 428: 427: 419: 415: 408: 395: 394: 387: 382: 374:Sampling design 369:Poisson process 355: 329: 324: 323: 299: 294: 293: 267: 254: 238: 233: 232: 204: 203: 176: 171: 170: 141: 136: 135: 124: 94: 89: 88: 60: 55: 54: 48:Bernoulli trial 21: 12: 11: 5: 515: 513: 505: 504: 499: 489: 488: 483: 482: 475: 468: 460: 457: 456: 439: 426: 425: 413: 406: 384: 383: 381: 378: 377: 376: 371: 366: 361: 354: 351: 336: 332: 309: 306: 302: 291: 290: 279: 274: 270: 266: 261: 257: 253: 248: 245: 241: 217: 214: 211: 186: 183: 179: 148: 144: 123: 120: 101: 97: 67: 63: 13: 10: 9: 6: 4: 3: 2: 514: 503: 500: 498: 495: 494: 492: 481: 476: 474: 469: 467: 462: 461: 455: 453: 449: 445: 440: 437: 433: 423: 417: 414: 409: 403: 399: 392: 390: 386: 379: 375: 372: 370: 367: 365: 362: 360: 357: 356: 352: 350: 334: 330: 307: 304: 300: 277: 272: 268: 264: 259: 255: 251: 246: 243: 239: 231: 230: 229: 215: 212: 209: 200: 184: 181: 177: 168: 164: 146: 142: 133: 129: 121: 119: 117: 99: 95: 86: 85: 65: 61: 51: 49: 46: 42: 38: 34: 30: 26: 19: 452:expanding it 441: 416: 397: 292: 201: 166: 162: 131: 125: 82:first-order 81: 52: 32: 28: 22: 45:independent 33:PO sampling 491:Categories 444:statistics 380:References 41:population 331:π 301:π 269:π 265:× 256:π 240:π 213:≠ 178:π 143:π 62:π 353:See also 37:sampling 165:th and 130:of the 35:) is a 404:  442:This 422:(pdf) 448:stub 402:ISBN 23:In 493:: 400:. 388:^ 349:. 228:: 199:. 27:, 479:e 472:t 465:v 454:. 410:. 335:i 308:i 305:i 278:. 273:j 260:i 252:= 247:j 244:i 216:j 210:i 185:j 182:i 167:j 163:i 147:i 132:i 100:i 96:p 66:i 20:.

Index

Poisson disk sampling
survey methodology
sampling
population
independent
Bernoulli trial
inclusion probability
Bernoulli sampling
inclusion probability
Bernoulli sampling
Poisson distribution
Poisson process
Sampling design


ISBN
978-0-387-97528-3
(pdf)
Stub icon
statistics
stub
expanding it
v
t
e
Categories
Sampling techniques
Statistics stubs

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