Knowledge

Pseudomedian

Source đź“ť

339: 127: 181: 154: 224: 201: 73: 326:
W. Pratt, T. Cooper, and I. Kabir. Pseudomedian filter. Architectures and Algorithms for Digital Image Processing II, pages 34–43. Proc. SPIE 534, 1985.
244:
Like the set of medians, the pseudomedian is well defined for all probability distributions, even for the many distributions that lack modes or means.
380: 279: + 1 windows, find the maximum minimum and the minimum maximum. The pseudomedian is the average of these two quantities. 373: 288: 234: 404: 409: 78: 366: 44: 36: 238: 159: 132: 8: 32: 317:
Hollander, M. and Wolfe, D. A. (2014). Nonparametric Statistical Methods (3nd Ed.). p58
209: 186: 58: 40: 354: 253: 338: 28: 399: 350: 298: 237:, defined as the median of all of the midpoints of pairs of observations, is a 393: 293: 275: + 1. For each window, compute the minimum and maximum. Across all 346: 20: 267: + 1, the pseudomedian is defined as follows. Construct 226:
is a symmetric distribution, the pseudomedian coincides with the
227: 247: 212: 189: 162: 135: 81: 61: 271: + 1 sliding windows each of length  218: 195: 175: 148: 121: 67: 31:for data-sets and populations. It agrees with the 183:are independent, each with the same distribution 75:is defined to be a median of the distribution of 391: 374: 230:; otherwise this is not generally the case. 35:for symmetric data-sets or populations. In 381: 367: 248:Pseudomedian filter in signal processing 392: 333: 55:The pseudomedian of a distribution 13: 14: 421: 16:Statistical measure of centrality 337: 256:there is another definition of 122:{\displaystyle (Z_{1}+Z_{2})/2} 320: 311: 108: 82: 50: 1: 304: 263:For a time series of length 2 39:, the pseudomedian is also a 353:. You can help Knowledge by 7: 282: 10: 426: 332: 45:probability distributions 289:Hodges–Lehmann estimator 235:Hodges–Lehmann statistic 37:mathematical statistics 349:-related article is a 260:for discrete signals. 220: 197: 177: 150: 123: 69: 241:of the pseudomedian. 221: 198: 178: 176:{\displaystyle Z_{2}} 151: 149:{\displaystyle Z_{1}} 124: 70: 239:consistent estimator 210: 187: 160: 133: 79: 59: 258:pseudomedian filter 405:Summary statistics 216: 193: 173: 146: 119: 65: 41:location parameter 362: 361: 254:signal processing 219:{\displaystyle F} 196:{\displaystyle F} 68:{\displaystyle F} 417: 410:Statistics stubs 383: 376: 369: 341: 334: 327: 324: 318: 315: 225: 223: 222: 217: 202: 200: 199: 194: 182: 180: 179: 174: 172: 171: 155: 153: 152: 147: 145: 144: 128: 126: 125: 120: 115: 107: 106: 94: 93: 74: 72: 71: 66: 27:is a measure of 425: 424: 420: 419: 418: 416: 415: 414: 390: 389: 388: 387: 331: 330: 325: 321: 316: 312: 307: 285: 250: 211: 208: 207: 188: 185: 184: 167: 163: 161: 158: 157: 140: 136: 134: 131: 130: 111: 102: 98: 89: 85: 80: 77: 76: 60: 57: 56: 53: 17: 12: 11: 5: 423: 413: 412: 407: 402: 386: 385: 378: 371: 363: 360: 359: 342: 329: 328: 319: 309: 308: 306: 303: 302: 301: 299:Lulu smoothing 296: 291: 284: 281: 249: 246: 215: 192: 170: 166: 143: 139: 118: 114: 110: 105: 101: 97: 92: 88: 84: 64: 52: 49: 15: 9: 6: 4: 3: 2: 422: 411: 408: 406: 403: 401: 398: 397: 395: 384: 379: 377: 372: 370: 365: 364: 358: 356: 352: 348: 343: 340: 336: 335: 323: 314: 310: 300: 297: 295: 294:Median filter 292: 290: 287: 286: 280: 278: 274: 270: 266: 261: 259: 255: 245: 242: 240: 236: 231: 229: 213: 204: 190: 168: 164: 141: 137: 116: 112: 103: 99: 95: 90: 86: 62: 48: 46: 42: 38: 34: 30: 26: 22: 355:expanding it 344: 322: 313: 276: 272: 268: 264: 262: 257: 251: 243: 232: 205: 54: 25:pseudomedian 24: 18: 51:Description 394:Categories 347:statistics 305:References 29:centrality 21:statistics 283:See also 129:, where 228:median 33:median 23:, the 400:Means 345:This 206:When 351:stub 233:The 156:and 43:for 252:In 19:In 396:: 203:. 47:. 382:e 375:t 368:v 357:. 277:N 273:N 269:N 265:N 214:F 191:F 169:2 165:Z 142:1 138:Z 117:2 113:/ 109:) 104:2 100:Z 96:+ 91:1 87:Z 83:( 63:F

Index

statistics
centrality
median
mathematical statistics
location parameter
probability distributions
median
Hodges–Lehmann statistic
consistent estimator
signal processing
Hodges–Lehmann estimator
Median filter
Lulu smoothing
Stub icon
statistics
stub
expanding it
v
t
e
Categories
Means
Summary statistics
Statistics stubs

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

↑