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Static Public Member Functions | List of all members
MDD Class Reference
Math tools

Modify Distrete Distribution. More...

#include <qle/math/discretedistribution.hpp>

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Static Public Member Functions

static DiscreteDistribution convolve (const DiscreteDistribution &a, const DiscreteDistribution &b, Size buckets)
 
static DiscreteDistribution rebucketfixednumber (const DiscreteDistribution &a, Size buckets)
 
static DiscreteDistribution rebucketfixedstep (const DiscreteDistribution &a, Real step)
 
static DiscreteDistribution sum (const DiscreteDistribution &a, const DiscreteDistribution &b, Size buckets)
 
static DiscreteDistribution sumspecialunsorted (const DiscreteDistribution &a, const DiscreteDistribution &b, Real c)
 
static DiscreteDistribution sumspecial (const DiscreteDistribution &a, const DiscreteDistribution &b, Real c)
 
static DiscreteDistribution sumspecialright (const DiscreteDistribution &a, const DiscreteDistribution &b, Real c)
 
static DiscreteDistribution splicemezz (const DiscreteDistribution &a, const DiscreteDistribution &b, Real c)
 
static DiscreteDistribution scalarmultprob (const DiscreteDistribution &a, const Real &b)
 
static DiscreteDistribution scalarmultx (const DiscreteDistribution &a, const Real &b)
 
static DiscreteDistribution scalarshiftx (const DiscreteDistribution &a, const Real &b)
 
static DiscreteDistribution functionmax (const DiscreteDistribution &a, const Real &b)
 
template<class F >
static DiscreteDistribution function (F &, const DiscreteDistribution &a)
 
static DiscreteDistribution functionmin (const DiscreteDistribution &a, const Real &b)
 
static Real expectation (const DiscreteDistribution &a)
 
static Real stdev (const DiscreteDistribution &a)
 
static Real leftstdev (const DiscreteDistribution &a)
 
static Real print (const DiscreteDistribution &a, const ostringstream &o)
 
static Real probabilitymatch (const DiscreteDistribution &a, const DiscreteDistribution &b, Real c, bool forward)
 
static Real probabilitymatch (const DiscreteDistribution &a, const DiscreteDistribution &b, Real c)
 Probability matching with linear interpolation. More...
 

Detailed Description

Modify Distrete Distribution.

This class implements a set of operations on discrete disctributions, that involve one or two distributions.

Definition at line 93 of file discretedistribution.hpp.

Member Function Documentation

◆ convolve()

DiscreteDistribution convolve ( const DiscreteDistribution &  a,
const DiscreteDistribution &  b,
Size  buckets 
)
static

Convolution of two discrete distribution

Definition at line 66 of file discretedistribution.cpp.

66 {
67 //-------------------------------------------
68 vector<Distributionpair> result(buckets);
69
70 vector<Distributionpair> x1pm1 = a.get();
71 vector<Distributionpair> x2pm2 = b.get();
72 vector<Distributionpair> xpconvtemp;
73
74 for (Size i = 0; i < x1pm1.size(); i++) {
75 for (Size j = 0; j < x2pm2.size(); j++) {
76 Distributionpair xp(x1pm1[i].x_ + x2pm2[j].x_, x1pm1[i].y_ * x2pm2[j].y_);
77 xpconvtemp.push_back(xp);
78 // cout << i << " " << x1pm1[i].x_ << " " << x1pm1[i].y_ << " " << x2pm2[j].x_ << " " << x2pm2[j].y_ <<
79 // endl;
80 }
81 }
82
83 std::sort(xpconvtemp.begin(), xpconvtemp.end());
84 //---------
85 // rebucket
86 //---------
87
88 vector<Distributionpair> xpconv(buckets, Distributionpair(0.0, 0.0));
89
90 Real xmin = xpconvtemp.front().x_;
91 Real xmax = xpconvtemp.back().x_;
92 Real Bucketsize = (xmax - xmin) / buckets;
93 // cout << "Bucketsize " << Bucketsize << "xMax "<< xmax<< "xmin "<< xmin <<endl;
94
95 if (xmin == xmax) {
96 buckets = 1;
97 Bucketsize = 1.;
98 }
99
100 for (Size i = 0; i < buckets; i++) {
101 xpconv[i].x_ = xmin + i * Bucketsize;
102 }
103
104 for (Size j = 0; j < xpconvtemp.size(); j++) {
105 Size bucket = static_cast<Size>((xpconvtemp[j].x_ - xmin) / Bucketsize);
106 QL_REQUIRE(bucket <= buckets, "Number of buckets in Convolution incorrect");
107 if (bucket == buckets) {
108 bucket -= 1;
109 }
110
111 Real probs = xpconv[bucket].y_ + xpconvtemp[j].y_;
112
113 // deal with zero probability
114
115 if (probs < 1.0e-20) {
116 xpconv[bucket].y_ = 0.0;
117 xpconv[bucket].x_ += 0.0;
118 } else {
119 Real intermed = (xpconv[bucket].x_ * xpconv[bucket].y_ + xpconvtemp[j].x_ * xpconvtemp[j].y_) / probs;
120 xpconv[bucket].y_ += xpconvtemp[j].y_;
121 xpconv[bucket].x_ = intermed;
122 }
123
124 /*cout << j << " bucket " << bucket
125 << " " << xpconvtemp[j].x_
126 << " " << xpconvtemp[j].y_
127 << " " << xpconv[bucket].x_
128 << " " << xpconv[bucket].y_
129 << " Bucketsize " << Bucketsize
130 << " xmin "<< xmin
131 <<" xmax " << xmax
132 << " test "<<xpconv[bucket].x_ - xmin+(bucket)*Bucketsize
133 << endl;*/
134
135 /*QL_REQUIRE( (xpconv[bucket].x_ - xmin+(bucket)*Bucketsize > -1.0e-8) and
136 ( xmin+(bucket+1)*Bucketsize - xpconv[bucket].x_ > -1.0e-8 ),"Convolve:: Fell out of bucket "<< bucket)
137 */
138 }
139
140 /* for (Size i = 0; i < xpconv.size() ;i++){
141 cout << i << " " << i*Bucketsize << " " << xpconv[i].x_ << " "<< xpconv[i].y_ <<
142 endl;
143 }
144 */
145 return DiscreteDistribution(xpconv);
146}
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◆ rebucketfixednumber()

DiscreteDistribution rebucketfixednumber ( const DiscreteDistribution &  a,
Size  buckets 
)
static

Amend the discretization of the distribution such that the number of buckets is reduced to the given number.

Definition at line 149 of file discretedistribution.cpp.

149 {
150 //-------------------------------------------
151 vector<Distributionpair> xptemp = a.get();
152
153 std::sort(xptemp.begin(), xptemp.end());
154
155 Real xmin = xptemp.front().x_;
156 Real xmax = xptemp.back().x_;
157 Real Bucketsize = (xmax - xmin) / buckets;
158
159 if (xmin == xmax) {
160 buckets = 1;
161 Bucketsize = 1.;
162 }
163
164 //---------
165 // rebucket
166 //---------
167
168 vector<Distributionpair> xp(buckets, Distributionpair(0.0, 0.0));
169
170 // cout << "Bucketsize " << Bucketsize << "xMax "<< xmax<< "xmin "<< xmin <<endl;
171
172 for (Size i = 0; i < buckets; i++) {
173 xp[i].x_ = xmin + i * Bucketsize;
174 }
175
176 for (Size j = 0; j < xptemp.size(); j++) {
177 Size bucket = static_cast<Size>((xptemp[j].x_ - xmin) / Bucketsize);
178 QL_REQUIRE(bucket <= buckets, "Number of buckets in Rebucket incorrect");
179 if (bucket == buckets) {
180 bucket -= 1;
181 }
182
183 Real probs = xp[bucket].y_ + xptemp[j].y_;
184
185 // deal with zero probability
186
187 if (probs < 1.0e-30) {
188 xp[bucket].y_ = 0.0;
189 xp[bucket].x_ += 0.0;
190 } else {
191 Real intermed = (xp[bucket].x_ * xp[bucket].y_ + xptemp[j].x_ * xptemp[j].y_) / probs;
192 xp[bucket].y_ += xptemp[j].y_;
193 xp[bucket].x_ = intermed;
194 }
195 }
196
197 return DiscreteDistribution(xp);
198}
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◆ rebucketfixedstep()

DiscreteDistribution rebucketfixedstep ( const DiscreteDistribution &  a,
Real  step 
)
static

Amend the discretization of the distribution such that the distance of adjacent buckets is reduced to the given number.

Definition at line 201 of file discretedistribution.cpp.

201 {
202 //-------------------------------------------
203 vector<Distributionpair> xptemp = a.get();
204
205 std::sort(xptemp.begin(), xptemp.end());
206
207 Size buckets;
208 Real xmin = xptemp.front().x_;
209 Real xmax = xptemp.back().x_;
210
211 if (xmin == xmax) {
212 buckets = 1;
213 } else {
214 buckets = static_cast<Size>(ceil((xmax - xmin) / step));
215 }
216
217 //---------
218 // rebucket
219 //---------
220
221 vector<Distributionpair> xp(buckets, Distributionpair(0.0, 0.0));
222
223 // cout << "Bucketsize " << Bucketsize << "xMax "<< xmax<< "xmin "<< xmin <<endl;
224
225 for (Size i = 0; i < buckets; i++) {
226 xp[i].x_ = xmin + i * step;
227 }
228
229 for (Size j = 0; j < xptemp.size(); j++) {
230 Size bucket = static_cast<Size>((xptemp[j].x_ - xmin) / step);
231 QL_REQUIRE(bucket <= buckets, "Number of buckets in Rebucket incorrect");
232 if (bucket == buckets) {
233 bucket -= 1;
234 }
235
236 Real probs = xp[bucket].y_ + xptemp[j].y_;
237
238 // deal with zero probability
239
240 if (probs < 1.0e-30) {
241 xp[bucket].y_ = 0.0;
242 xp[bucket].x_ += 0.0;
243 } else {
244 Real intermed = (xp[bucket].x_ * xp[bucket].y_ + xptemp[j].x_ * xptemp[j].y_) / probs;
245 xp[bucket].y_ += xptemp[j].y_;
246 xp[bucket].x_ = intermed;
247 }
248 }
249
250 return DiscreteDistribution(xp);
251}
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◆ sum()

DiscreteDistribution sum ( const DiscreteDistribution &  a,
const DiscreteDistribution &  b,
Size  buckets 
)
static

Add two discrete distributions while introducing a desired number of buckets.

Definition at line 254 of file discretedistribution.cpp.

254 {
255 //-------------------------------------------
256
257 vector<Distributionpair> x1pm1 = a.get();
258 vector<Distributionpair> x2pm2 = b.get();
259 vector<Distributionpair> xpsumtemp;
260
261 for (Size i = 0; i < x1pm1.size(); i++) {
262 Distributionpair xp(x1pm1[i].x_, x1pm1[i].y_);
263 xpsumtemp.push_back(xp);
264 }
265
266 for (Size i = 0; i < x2pm2.size(); i++) {
267 Distributionpair xp(x2pm2[i].x_, x2pm2[i].y_);
268 xpsumtemp.push_back(xp);
269 }
270
271 std::sort(xpsumtemp.begin(), xpsumtemp.end());
272 //---------
273 // rebucket
274 //---------
275
276 vector<Distributionpair> xpsum(buckets, Distributionpair(0.0, 0.0));
277
278 Real xmin = xpsumtemp.front().x_;
279 Real xmax = xpsumtemp.back().x_;
280 Real Bucketsize = (xmax - xmin) / buckets;
281 // cout << "Bucketsize " << Bucketsize << "xMax "<< xmax<< "xmin "<< xmin <<endl;
282
283 if (xmin == xmax) {
284 xpsum[0].x_ = xmin;
285 xpsum[0].y_ = 1.0;
286 } else {
287 for (Size i = 0; i < buckets; i++) {
288 xpsum[i].x_ = i * Bucketsize;
289 }
290
291 for (Size j = 0; j < xpsumtemp.size(); j++) {
292 Size bucket = static_cast<Size>((xpsumtemp[j].x_ - xmin) / Bucketsize);
293 QL_REQUIRE(bucket <= buckets, "Number of buckets in Convolution incorrect: " << bucket);
294 if (bucket == buckets) {
295 bucket -= 1;
296 }
297
298 Real probs = xpsum[bucket].y_ + xpsumtemp[j].y_;
299
300 // deal with zero probability
301
302 if (probs < 1.0e-30) {
303 xpsum[bucket].y_ = 0.0;
304 xpsum[bucket].x_ += 0.0;
305 } else {
306 Real intermed = (xpsum[bucket].x_ * xpsum[bucket].y_ + xpsumtemp[j].x_ * xpsumtemp[j].y_) / probs;
307 xpsum[bucket].y_ += xpsumtemp[j].y_;
308 xpsum[bucket].x_ = intermed;
309 }
310
311 /*cout << j << " bucket " << bucket << " " <<
312 xpsumtemp[j].x_ << " " <<
313 xpsumtemp[j].y_ << " " <<
314 xpsum[bucket].x_ << " " <<
315 xpsum[bucket].y_ <<
316 endl; */
317 }
318
319 /* for (Size i = 0; i < xpsum.size() ;i++){
320 cout << i << " " << i*Bucketsize << " " << xpsum[i].x_ << " "<< xpsum[i].y_ <<
321 endl;
322 }
323 */
324 }
325 return DiscreteDistribution(xpsum);
326}
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◆ sumspecialunsorted()

DiscreteDistribution sumspecialunsorted ( const DiscreteDistribution &  a,
const DiscreteDistribution &  b,
Real  c 
)
static

Add c * distribution b to distribution a, starting from the left.

Definition at line 408 of file discretedistribution.cpp.

408 {
409 //-------------------------------------------
410
411 vector<Distributionpair> x1pm1 = a.get();
412 vector<Distributionpair> x2pm2 = b.get();
413 Real c_ = c;
414 vector<Distributionpair> xpsumtemp;
415
416 // std::sort (x1pm1.begin(), x1pm1.end());
417 // std::sort (x2pm2.begin(), x2pm2.end());
418
419 Real cumLast = 0.0;
420 Real cumNow = 0.0;
421
422 for (Size i = 0; i < x2pm2.size(); i++) {
423 cumNow += x2pm2[i].y_;
424 Real cumX1 = 0.0;
425 for (Size j = 0; j < x1pm1.size(); j++) {
426 cumX1 += x1pm1[j].y_;
427 if ((cumX1 > cumLast) && (cumX1 <= cumNow)) {
428 x1pm1[j].x_ += x2pm2[i].x_ * c_;
429 }
430 }
431 // cout<<"Cum X1"<< cumX1<<" Cum now" << cumNow<<endl;
432 // QL_REQUIRE( cumNow <= cumX1, "Cumulative probability of Distribution b exceeds a");
433 cumLast = cumNow;
434 }
435 return x1pm1;
436}
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◆ sumspecial()

DiscreteDistribution sumspecial ( const DiscreteDistribution &  a,
const DiscreteDistribution &  b,
Real  c 
)
static

Add c * distribution b to distribution a, starting from the right.

Definition at line 439 of file discretedistribution.cpp.

439 {
440 //-------------------------------------------
441
442 vector<Distributionpair> x1pm1 = a.get();
443 vector<Distributionpair> x2pm2 = b.get();
444 Real c_ = c;
445 vector<Distributionpair> xpsumtemp;
446
447 std::sort(x1pm1.begin(), x1pm1.end());
448 std::sort(x2pm2.begin(), x2pm2.end());
449
450 Real cumLast = 0.0;
451 Real cumNow = 0.0;
452
453 for (Size i = 0; i < x2pm2.size(); i++) {
454 cumNow += x2pm2[i].y_;
455 Real cumX1 = 0.0;
456 for (Size j = 0; j < x1pm1.size(); j++) {
457 cumX1 += x1pm1[j].y_;
458 if ((cumX1 >= cumLast) && (cumX1 < cumNow)) {
459 x1pm1[j].x_ += x2pm2[i].x_ * c_;
460 }
461 }
462 // cout<<"Cum X1"<< cumX1<<" Cum now" << cumNow<<endl;
463 // QL_REQUIRE( cumNow <= cumX1, "Cumulative probability of Distribution b exceeds a");
464 cumLast = cumNow;
465 }
466 return x1pm1;
467}
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◆ sumspecialright()

DiscreteDistribution sumspecialright ( const DiscreteDistribution &  a,
const DiscreteDistribution &  b,
Real  c 
)
static

TODO

Definition at line 470 of file discretedistribution.cpp.

470 {
471 //-------------------------------------------
472
473 vector<Distributionpair> x1pm1 = a.get();
474 vector<Distributionpair> x2pm2 = b.get();
475 Real c_ = c;
476 vector<Distributionpair> xpsumtemp;
477
478 std::sort(x1pm1.begin(), x1pm1.end());
479 std::sort(x2pm2.begin(), x2pm2.end());
480
481 Real cumLast = 0.0;
482 Real cumNow = 0.0;
483
484 for (Size i = x2pm2.size(); i > 0; i--) {
485 cumNow += x2pm2[i - 1].y_;
486 Real cumX1 = 0.0;
487 for (Size j = x1pm1.size(); j > 0; j--) {
488 cumX1 += x1pm1[j - 1].y_;
489 if ((cumX1 >= cumLast) && (cumX1 < cumNow)) {
490 x1pm1[j - 1].x_ += x2pm2[i - 1].x_ * c_;
491 }
492 }
493 // cout<<"Cum X1"<< cumX1<<" Cum now" << cumNow<<endl;
494 // QL_REQUIRE( cumNow <= cumX1, "Cumulative probability of Distribution b exceeds a");
495 cumLast = cumNow;
496 }
497 return x1pm1;
498}
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◆ splicemezz()

DiscreteDistribution splicemezz ( const DiscreteDistribution &  a,
const DiscreteDistribution &  b,
Real  c 
)
static

TODO

Definition at line 501 of file discretedistribution.cpp.

501 {
502 //-------------------------------------------
503
504 vector<Distributionpair> x1pm1 = a.get();
505 vector<Distributionpair> x2pm2 = b.get();
506 vector<Distributionpair> xpsumtemp;
507 Real probmNNzero = 0.;
508 Real probKicker = 0.;
509
510 // Splices together the mezz and equity distributions to form the kicker
511
512 for (Size i = 0; i < x1pm1.size(); i++) {
513
514 Distributionpair xp(x1pm1[i].x_, x1pm1[i].y_);
515 if (x1pm1[i].x_ >= 0) {
516 xpsumtemp.push_back(xp);
517 } else {
518 probmNNzero += x1pm1[i].y_;
519 }
520 }
521
522 for (Size i = 0; i < x2pm2.size(); i++) {
523 Distributionpair xp((1. - kR) * x2pm2[i].x_, x2pm2[i].y_);
524 if (x2pm2[i].x_ < 0) {
525 xpsumtemp.push_back(xp);
526 probKicker += x2pm2[i].y_;
527 }
528 }
529 Distributionpair xp(0.0, probmNNzero - probKicker);
530 QL_REQUIRE(xp.y_ >= 0, "Problem with probabilities in Mezz Splice");
531 xpsumtemp.push_back(xp);
532
533 std::sort(xpsumtemp.begin(), xpsumtemp.end());
534
535 return DiscreteDistribution(xpsumtemp);
536}
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◆ scalarmultprob()

DiscreteDistribution scalarmultprob ( const DiscreteDistribution &  a,
const Real &  b 
)
static

Scale each density by factor b.

Definition at line 539 of file discretedistribution.cpp.

539 {
540 //-------------------------------------------
541
542 vector<Distributionpair> x1pm1 = a.get();
543 Real b_ = b;
544 vector<Distributionpair> scalarmult;
545
546 for (Size i = 0; i < x1pm1.size(); i++) {
547
548 Distributionpair xp(x1pm1[i].x_, x1pm1[i].y_ * b_);
549 scalarmult.push_back(xp);
550 }
551 return DiscreteDistribution(scalarmult);
552}
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◆ scalarmultx()

DiscreteDistribution scalarmultx ( const DiscreteDistribution &  a,
const Real &  b 
)
static

Scale each coordinate by factor x.

Definition at line 555 of file discretedistribution.cpp.

555 {
556 //-------------------------------------------
557
558 vector<Distributionpair> x1pm1 = a.get();
559 Real b_ = b;
560 vector<Distributionpair> scalarmult;
561
562 for (Size i = 0; i < x1pm1.size(); i++) {
563
564 Distributionpair xp(b_ * x1pm1[i].x_, x1pm1[i].y_);
565 scalarmult.push_back(xp);
566 }
567 return DiscreteDistribution(scalarmult);
568}
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◆ scalarshiftx()

DiscreteDistribution scalarshiftx ( const DiscreteDistribution &  a,
const Real &  b 
)
static

Shift each coordinate by amount b.

Definition at line 571 of file discretedistribution.cpp.

571 {
572 //-------------------------------------------
573
574 vector<Distributionpair> x1pm1 = a.get();
575 Real b_ = b;
576 vector<Distributionpair> scalarmult;
577
578 for (Size i = 0; i < x1pm1.size(); i++) {
579
580 Distributionpair xp(x1pm1[i].x_ + b_, x1pm1[i].y_);
581 scalarmult.push_back(xp);
582 }
583 return DiscreteDistribution(scalarmult);
584}
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◆ functionmax()

DiscreteDistribution functionmax ( const DiscreteDistribution &  a,
const Real &  b 
)
static

CHECK: Cut off the branch of the distribution to the left of coordinate b and subsitute it with a single oint at coordinate b holding the cumulative probability up to b.

Definition at line 587 of file discretedistribution.cpp.

587 {
588 //-------------------------------------------
589
590 vector<Distributionpair> x1pm1 = a.get();
591 Real b_ = b;
592 vector<Distributionpair> func;
593
594 std::sort(x1pm1.begin(), x1pm1.end());
595
596 Real temp = 0.;
597
598 for (Size i = 0; i < x1pm1.size(); i++) {
599 if (x1pm1[i].x_ <= b_) {
600 temp += x1pm1[i].y_;
601 }
602 }
603 Distributionpair xp(b_, temp);
604 func.push_back(xp);
605
606 for (Size i = 0; i < x1pm1.size(); i++) {
607 if (x1pm1[i].x_ > b_) {
608 Distributionpair xp(max(x1pm1[i].x_, b_), x1pm1[i].y_);
609 func.push_back(xp);
610 }
611 }
612
613 return DiscreteDistribution(func);
614}
QuantExt::max
CompiledFormula max(CompiledFormula x, const CompiledFormula &y)
Definition: compiledformula.cpp:159
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◆ function()

DiscreteDistribution function ( F &  f,
const DiscreteDistribution &  a 
)
static

Apply function F to each coordinate.

Definition at line 191 of file discretedistribution.hpp.

191 {
192 vector<Distributionpair> x1pm1 = a.get();
193 vector<Distributionpair> func;
194
195 for (Size i = 0; i < x1pm1.size(); i++) {
196 Distributionpair xp(f(x1pm1[i].x_), x1pm1[i].y_);
197 func.push_back(xp);
198 }
199 return DiscreteDistribution(func);
200}
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◆ functionmin()

DiscreteDistribution functionmin ( const DiscreteDistribution &  a,
const Real &  b 
)
static

TODO

Definition at line 617 of file discretedistribution.cpp.

617 {
618 //-------------------------------------------
619
620 vector<Distributionpair> x1pm1 = a.get();
621 Real b_ = b;
622 vector<Distributionpair> func;
623
624 std::sort(x1pm1.begin(), x1pm1.end());
625
626 for (Size i = 0; i < x1pm1.size(); i++) {
627 if (x1pm1[i].x_ < b_) {
628 Distributionpair xp(min(x1pm1[i].x_, b_), x1pm1[i].y_);
629 func.push_back(xp);
630 }
631 }
632
633 Real temp = 0.;
634
635 for (Size i = 0; i < x1pm1.size(); i++) {
636 if (x1pm1[i].x_ >= b_) {
637 temp += x1pm1[i].y_;
638 }
639 }
640 Distributionpair xp(b_, temp);
641 func.push_back(xp);
642
643 return DiscreteDistribution(func);
644}
QuantExt::min
CompiledFormula min(CompiledFormula x, const CompiledFormula &y)
Definition: compiledformula.cpp:162
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◆ expectation()

Real expectation ( const DiscreteDistribution &  a)
static

Return the expected coordinate value.

Definition at line 647 of file discretedistribution.cpp.

647 {
648 //-------------------------------------------
649
650 vector<Distributionpair> x1pm1 = a.get();
651 Real exp = 0.0;
652
653 for (Size i = 0; i < x1pm1.size(); i++) {
654
655 exp += x1pm1[i].x_ * x1pm1[i].y_;
656 }
657 return exp;
658}
QuantExt::exp
CompiledFormula exp(CompiledFormula x)
Definition: compiledformula.cpp:151
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◆ stdev()

Real stdev ( const DiscreteDistribution &  a)
static

Return the standard deviation of the discrete distribution.

Definition at line 661 of file discretedistribution.cpp.

661 {
662 //-------------------------------------------
663
664 vector<Distributionpair> x1pm1 = a.get();
665 Real mu = MDD::expectation(a);
666 Real variance = 0.0;
667
668 for (Size i = 0; i < x1pm1.size(); i++) {
669
670 variance += pow((x1pm1[i].x_ - mu), 2) * x1pm1[i].y_;
671 }
672 Real stdev = sqrt(variance);
673 return stdev;
674}
QuantExt::MDD::expectation
static Real expectation(const DiscreteDistribution &a)
Definition: discretedistribution.cpp:647
QuantExt::MDD::stdev
static Real stdev(const DiscreteDistribution &a)
Definition: discretedistribution.cpp:661
QuantExt::sqrt
RandomVariable sqrt(RandomVariable x)
Definition: randomvariable.cpp:771
QuantExt::variance
RandomVariable variance(const RandomVariable &r)
Definition: randomvariable.cpp:1281
QuantExt::pow
CompiledFormula pow(CompiledFormula x, const CompiledFormula &y)
Definition: compiledformula.cpp:165
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◆ leftstdev()

Real leftstdev ( const DiscreteDistribution &  a)
static

TODO

Definition at line 677 of file discretedistribution.cpp.

677 {
678 //-------------------------------------------
679
680 vector<Distributionpair> x1pm1 = a.get();
681 Real mu = MDD::expectation(a);
682 Real variance = 0.0;
683
684 for (Size i = 0; i < x1pm1.size(); i++) {
685 if (x1pm1[i].x_ - mu < 0.0)
686 variance += pow((x1pm1[i].x_ - mu), 2) * x1pm1[i].y_;
687 }
688 Real stdev = sqrt(variance);
689 return stdev;
690}
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◆ print()

Real print ( const DiscreteDistribution &  a,
const ostringstream &  o 
)
static

Print the distribution of the provided stream.

Definition at line 693 of file discretedistribution.cpp.

693 {
694 //-------------------------------------------
695
696 ofstream file;
697 file.open(o.str().c_str());
698 if (!file.is_open())
699 QL_FAIL("error opening file " << o.str());
700 file.setf(ios::scientific, ios::floatfield);
701 file.setf(ios::showpoint);
702 file.precision(4);
703 for (Size k = 0; k < a.size(); k++) {
704 file << k << " " << a.get(k).x_ << " " << a.get(k).y_ << endl;
705 }
706 file.close();
707
708 return 0;
709}
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◆ probabilitymatch() [1/2]

Real probabilitymatch ( const DiscreteDistribution &  a,
const DiscreteDistribution &  b,
Real  c,
bool  forward 
)
static

Probability matching:

Compute the cumulative probability P_b(c) of distribution b up to the provided coordintae c.

Compute the coordinate c* of distribution a where its cumulative probability equals P_b(c), i.e. P_a(c*) = P_b(c).

Return coordinate c*.

Definition at line 328 of file discretedistribution.cpp.

328 {
329 //-------------------------------------------
330
331 vector<Distributionpair> x1pm1 = a.get();
332 vector<Distributionpair> x2pm2 = b.get();
333 Real c_ = c;
334 Real target(0.);
335 std::sort(x2pm2.begin(), x2pm2.end());
336 if (forward) {
337 std::sort(x1pm1.begin(), x1pm1.end());
338 } else {
339 std::sort(x1pm1.rbegin(), x1pm1.rend());
340 }
341 Real cuma = 0.0;
342 Real cumb = 0.0;
343
344 for (Size i = 0; i < x2pm2.size(); i++) {
345 if (x2pm2[i].x_ <= c_) {
346 cumb += x2pm2[i].y_;
347 }
348 }
349 for (Size i = 0; i < x1pm1.size(); i++) {
350 cuma += x1pm1[i].y_;
351 if (cuma <= cumb) {
352 target = x1pm1[i].x_;
353 }
354 }
355
356 return target;
357}
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◆ probabilitymatch() [2/2]

Real probabilitymatch ( const DiscreteDistribution &  a,
const DiscreteDistribution &  b,
Real  c 
)
static

Probability matching with linear interpolation.

Definition at line 359 of file discretedistribution.cpp.

359 {
360
361 // Sort both distributions and calculate their cumulative distributions
362 vector<Distributionpair> aData = a.get();
363 vector<Distributionpair> bData = b.get();
364 sort(aData.begin(), aData.end());
365 sort(bData.begin(), bData.end());
366
367 // Find P_b(c)
368 Real probability = 0.0;
369 Distributionpair dummy(c);
370 vector<Distributionpair>::iterator itVar = lower_bound(bData.begin(), bData.end(), dummy);
371 if (itVar == bData.end()) {
372 for (Size i = 0; i < bData.size(); i++)
373 probability += bData[i].y_;
374 } else if (itVar == bData.begin()) {
375 probability = itVar->y_;
376 } else {
377 Size startIndex = itVar - bData.begin() - 1;
378 for (Size i = 0; i <= startIndex; i++)
379 probability += bData[i].y_;
380 probability += (c - bData[startIndex].x_) * itVar->y_ / (itVar->x_ - bData[startIndex].x_);
381 }
382
383 // Find target such that P_a(target) = P_b(c)
384 Real sum = 0.0;
385 vector<Real> aCumulative(aData.size());
386 vector<Real> aValues(aData.size());
387 for (Size i = 0; i < aData.size(); i++) {
388 sum += aData[i].y_;
389 aCumulative[i] = sum;
390 aValues[i] = aData[i].x_;
391 }
392
393 vector<Real>::iterator itProb = lower_bound(aCumulative.begin(), aCumulative.end(), probability);
394 if (itProb == aCumulative.end()) {
395 return aValues.back();
396 } else if (itProb == aCumulative.begin()) {
397 return aValues.front();
398 } else {
399 Size low = itProb - aCumulative.begin() - 1;
400 Real target = aValues[low];
401 target += (aValues[low + 1] - aValues[low]) * (probability - aCumulative[low]) /
402 (aCumulative[low + 1] - aCumulative[low]);
403 return target;
404 }
405}
QuantExt::MDD::sum
static DiscreteDistribution sum(const DiscreteDistribution &a, const DiscreteDistribution &b, Size buckets)
Definition: discretedistribution.cpp:254
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